Séminaire sur les Singularités des Surfaces.
Lecture Notes in Mathematics, 777, Demazure, M. & Pinkham, H. C. & Teissier, B.
Held at the Centre de Mathématiques de l'Ecole Polytechnique, Palaiseau, 1976--1977,
Springer, Berlin, viii+339, 1980.
Algebraic surfaces.
By the members of the seminar of I. R. Safarevic.
Translated from the Russian by Susan Walker.
Translation edited, with supplementary material, by K. Kodaira & D. C.
Spencer.
Proceedings of the Steklov Institute of Mathematics,
No. 75 (1965), American Mathematical Society, Providence, R.I., ix+281, 1965.
M. Alberich-Carraminana. Geometry of the plane Cremona maps.
Lecture Notes in Mathematics, 1769, Springer-Verlag, Berlin, xvi+257, 2002.
M. Alberich-Carraminana. Plane Cremona maps, exceptional curves and roots.
Trans. Amer. Math. Soc. 357, no. 5, 1901--1914 (electronic), 2005.
J. W. Alexander. On the factorization of Cremona plane transformations.
Trans. Amer. Math. Soc., 17, 3, 295--300, 1916. pdf
E. Angelini & M. Mella. The action of the Cremona group on rational curves of $\mathbb{P}^3$. pdf
S. Asgarli, K.-W. Lai, M. Nakahara & S. Zimmermann. Biregular Cremona transformations of the plane. pdf
D. Avritzer, G. Gonzalez-Sprinberg & I. Pan. On Cremona transformations and quadratic complexes.
Rend. Circ. Mat. Palermo (2) 57 (2008), no. 3, 353--375. pdf
D. Avritzer, G. Gonzalez-Sprinberg & I. Pan. On singular quadratic complexes, quintic curves and Cremona transformations.
Rend. Circ. Mat. Palermo (2) 61 (2012), no. 2, 201--240. pdf
L. Bayle & A. Beauville. Birational involutions of P2.
Kodaira's issue, Asian J. Math., 4, 1, 11--17, 2000. pdf
T. Bayraktar & S. Cantat. Constraints on automorphism groups of higher dimensional manifolds.
J. Math. Anal. Appl. 405 (2013), no. 1, 209--213. pdf
A. Beauville. p-elementary subgroups of the Cremona group.
A. Beauville. Endomorphisms of hypersurfaces and other manifolds.
Internat. Math. Res. Notices 2001, no. 1, 53--58. pdf
A. Beauville & J. Blanc. On Cremona transformations of prime order. C. R. Math.
Acad. Sci. Paris, 339, 4, 257--259, 2004. pdf
E. Bedford. The Dynamical Degrees of a Mapping. arXiv:1110.1741
E. Bedford & J. Diller. Energy and invariant measures for birational surface maps. Duke Math. J., 128, 2, 331--368, 2005. pdf
E. Bedford, S. Cantat & K. Kim. Pseudo-automorphisms with no invariant foliation.
J. Mod. Dyn. 8 (2014), no. 2, 221--250. pdf
E. Bedford & K. Kim. Dynamics of (pseudo) automorphisms of 3-space: periodicity versus positive entropy.
Publ. Mat. 58 (2014), no. 1, 65--119. pdf
E. Bedford & K. Kim. On the Degree Growth of Birational Mappings in Higher Dimension. math.DS/0406621
E. Bedford & K. Kim. Periodicities in Linear Fractional Recurrences: Degree growth of birational surface maps.
Michigan Math. J. 54 (2006), no. 3, 647--670. pdf
E. Bedford & K. Kim. Degree growth of matrix inversion: birational maps of symmetric, cyclic matrices.
Discrete Contin. Dyn. Syst. 21 (2008), no. 4, 977--1013. pdf
E. Bedford & K. Kim. Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences.
J. Geom. Anal. 19 (2009), no. 3, 553--583. pdf
E. Bedford, K. Kim, T.T. Truong, N.
Abarenkova & J.-M. Maillard. Degree complexity of a family of birational maps.
Math. Phys. Anal. Geom., 11, 1, 53--71, 2008. pdf
E. Bedford & K. Kim. Linear Recurrences in the Degree Sequences of Monomial Mappings.
Ergodic Theory Dynam. Systems 28 (2008), no. 5, 1369--1375. pdf
E. Bedford & K. Kim. Continuous Families of Rational Surface Automorphisms with Positive Entropy.
Math. Ann. 348 (2010), no. 3, 667--688. pdf
E. Bedford & K. Kim. Dynamics of Rational Surface Automorphisms: Rotation Domains.
Amer. J. Math. 134 (2012), no. 2, 379--405. pdf
E. Bedford & T. T. Truong. Degree Complexity of Birational Maps Related to Matrix Inversion.
Comm. Math. Phys. 298 (2010), no. 2, 357–368.
J. Bell & J. Diller & M. Jonsson. A transcendental dynamical degree. pdf
E. Bertini. Ricerche sulle trasformazioni univoche involutorie nel piano.
Annali di Mat., 8, 244--286, 1877.
C. Bisi, A. Calabri & M. Mella. On Plane Cremona Transformations of Fixed Degree.
J. Geom. Anal. 25 (2015), no. 2, 1108--1131. pdf
C. Bisi, J.-P. Furter & S. Lamy. The tame automorphism group of an affine quadric threefold acting on a square complex.
J. Éc. polytech. Math. 1 (2014), 161--223. pdf
J. Blanc. Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces. pdf
J. Blanc. Symplectic birational transformations of the plane.
Osaka J. Math. 50 (2013), no. 2, 573--590. pdf
J. Blanc. Simple relations in the Cremona group.
Proc. Amer. Math. Soc. 140 (2012), no. 5, 1495--1500. pdf
J. Blanc. Groupe de Cremona, connexité et simplicité.
Ann. Sci. Éc. Norm. Supér., 43, fascicule 2 (2010), 357--364 pdf
J. Blanc. Algebraic elements of the Cremona groups.
From classical to modern algebraic geometry, 351--360, Trends Hist. Sci., Birkhäuser/Springer, Cham, 2016. pdf
J. Blanc & S. Cantat. Dynamical degrees of birational transformations of projective surfaces.
Indiana Univ. Math. J. 62 (2013), no. 4, 1143--1164. pdf
J. Blanc. The correspondance between a plane curve and its complement.
J. Reine. Angew. Math. 633 (2009), 1--10 pdf
J. Blanc. Elements and cyclic subgroups of finite order of the Cremona group.
Comment. Math. Helv. 86 (2011), no. 2, 469--497. pdf
J. Blanc. Linearisation of finite abelian subgroups of the Cremona group of
the plane.
Groups Geom. Dyn. 3 (2009), no. 2, 215--266. pdf
J. Blanc. Conjugacy classes of affine automorphisms of Kn
and linear automorphisms of Pn in the Cremona groups.
Manuscripta Math., 119, 2006, 2, 225--241. pdf
J. Blanc. On the inertia group of elliptic curves in the
Cremona group
of the plane. Michigan Math. J., 56, 2, 315--330, 2008. pdf
J. Blanc. The number of conjugacy classes of elements of the Cremona group of some given finite order.
Bull. Soc. Math. France, 135, 3, 419--434, 2007. pdf
J. Blanc. Sous-groupes algébriques du groupe de Cremona.
Transform. Groups 14 (2009), no. 2, 249--285. pdf
J. Blanc, I. Pan & T.
Vust. Sur un théorème de
Castelnuovo. Bull. Braz. Math. Soc. (N.S.), 39, 1, 61--80, 2008.
pdf
J. Blanc, E. Yasinsky. Quotients of groups of birational transformations of cubic del Pezzo fibrations. pdf
J. Blanc, I. Pan
& T. Vust. On birational transformation of pairs in the complex plane..
Geom. Dedicata 139 (2009), 57--73. pdf
J. Blanc & J. Déserti. Embeddings of SL(2,Z) into the Cremona group.
Transform. Groups 17 (2012), no. 1, 21--50. pdf
J. Blanc & J. Déserti. Degree growth of birational maps of the plane.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 2, 507--533. arXiv:1109.6810
J. Blanc, J.-P. Furter & M. Hemmig. Exceptional isomorphisms between complements of affine plane curves. pdf
J. Blanc. Finite abelian subgroups of the Cremona group of the plane.
C. R. Math. Acad. Sci. Paris 344 (2007), no. 1, 21--26. pdf
J. Blanc, S. Lamy & S. Zimmermann. Quotients of higher dimensional Cremona groups. pdf
J. Blanc & S. Zimmermann. Topological simplicity of the Cremona groups.
Amer. J. Math. 140 (2018), no. 5, 1297--1309. pdf
J. Blanc & J.-P. Furter. Topologies and scructures of the Cremona groups.
Ann. of Math. (2) 178 (2013), no. 3, 1173--1198. pdf
J. Blanc & J.-P. Furter. Length in the Cremona group.
Ann. H. Lebesgue 2 (2019), 187--257. pdf
J. Blanc & S. Lamy. Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links.
Proc. Lond. Math. Soc. (3) 105 (2012), no. 5, 1047--1075. pdf
J. Blanc & S. Lamy. On birational maps from cubic threefolds.
North-West. Eur. J. Math. 1 (2015), 55--84. pdf
J. Blanc & I. Heden. The group of Cremona transformations generated by linear maps and the standard involution.
Ann. Inst. Fourier (Grenoble) 65 (2015), no. 6, 2641--2680. pdf
Y. Bodnarchuk. Every regular automorphism of the affine Cremona group is inner.
J. Pure Appl. Algebra 157, no. 1, 115--119, 2001.
C. J. Bott, S. Hamid Hassanzadeh, K. Schwede & D. Smolkin. Rational maps, a package for Macaulay 2. pdf
A. Calabri & C. Ciliberto. On Cremona contractibility of unions of lines in the plane. pdf
G. Call & J. Silverman. Degenaration of dynamical degrees in families of maps. pdf
S. Cantat, Birational permutations.
C. R. Math. Acad. Sci. Paris 347 (2009), no. 21-22, 1289--1294. pdf.
S. Cantat, Sur les groupes de transformations birationnelles des surfaces, preprint, 2006. pdf.
S. Cantat, The Cremona group in two variables. pdf.
S. Cantat, Morphisms between Cremona groups and characterization of rational varieties.
Compos. Math. 150 (2014), no. 7, 1107--1124. pdf.
S. Cantat & V. Guirardel & A. Lonjou. Elements generating a proper normal subgroup of the Cremona group. pdf.
S. Cantat & C. Favre. Symétries birationnelles des surfaces feuilletées. J. Reine Angew. Math., 561, 199--235, 2003. pdf, erratum.
S. Cantat & S. Lamy. Groupes d'automorphismes polynomiaux du plan. Geom. Dedicata, 123, 201--221, 2006.
pdf
S. Cantat & S. Lamy. Normal subgroups of the Cremona group.
Acta Math. 210 (2013), no. 1, 31--94. long preliminary version
S. Cantat & J. Xie. Algebraic actions of discrete groups: the p-adic method.
Acta Math. 220 (2018), no. 2, 239--295. pdf
S. Cantat & J. Xie. On degrees of birational mappings. pdf
S. Cantat & Y. de Cornulier. Distortion in Cremona groups. pdf
S. Cantat & Y. de Cornulier. Commensurating actions of birational groups and group of pseudo-automorphisms. pdf
G. Castelnuovo. Sulle transformazioni cremoniane del piano, che ammettono una curva
fiera.
Rend. Accad. Lincei, 1892.
G. Castelnuovo. Le trasformationi generatrici del gruppo
cremoniano nel piano.
Atti della R. Accad. delle Scienze di Torino, 36, 861--874, 1901.
D. Cerveau & J. Déserti. Transformations birationnelles de petit degré.
Cours Spécialisés, Société Mathématique de France, 19 (2013), viii+ 223 pages pdf
D. Cerveau & J. Déserti. Feuilletages et transformations périodiques.
Experiment. Math. 19 (2010), no. 3, 447--464 pdf
D. Cerveau & J. Déserti. Centralisateurs dans le groupe de Jonquières.
Michigan Math. J., 61, (2012), 763--783 pdf
D. Cerveau & J. Déserti. Action of the Cremona group on foliations on $\mathbb{P}^2_\mathbb{C}$: some curious facts.
Forum Math. 27 (2015), no. 6, 3697--3715. pdf
D. Cerveau & J. Déserti. Birational maps preserving the contact structure on $\mathbb{P}^3_\mathbb{C}$. pdf
W. K. Clifford. Analysis of Cremona's transformations.
Kodaira's issue, Math. Papers, MacMillan, London, 538--542, 1882.
I. Cheltsov & C. Shramov. Five embeddings of one simple group. arXiv:0910.1783
I. Cheltsov & C. Shramov. Three embeddings of the Klein simple group into the Cremona group of rank three. arXiv:1010.1918
A. B. Coble. Algebraic geometry and theta functions. Revised printing. American Mathematical Society Colloquium
Publication, vol. X, American Mathematical Society, Providence, R.I., vii+282, 1961.
A. B. Coble. Cremona transformations with an invariant rational sextic.
Bull. Amer. Math. Soc. 45, no. 4, 285--288, 1939.
A. B. Coble. Groups of Cremona transformations in space of planar type.
Duke Math. J. 2 (1936), no. 1, 1--9.
A. B. Coble. Groups of Cremona transformations in space of planar type. II.
Duke Math. J. 2 (1936), no. 2, 205--219.
A. B. Coble. A Generalization of the Weddle Surface, of Its Cremona Group, and of Its Parametric Expression in Terms of Hyperelliptic Theta Functions.
Amer. J. Math. 52, no. 3, 439--500, 1930.
A. B. Coble. Cremona transformations and applications to algebra, geometry, and modular functions.
Bull. Amer. Math. Soc. 28, no. 7, 329--364, 1922.
A. B. Coble. Point sets and allied Cremona groups. I.
Trans. Amer. Math. Soc. 16(1915), no. 2, 155--198.
A. B. Coble. Point sets and allied Cremona groups. II.
Trans. Amer. Math. Soc. 17(1916), no. 3, 345--385, 1916.
A. B. Coble. Point sets and allied Cremona groups. III.
Trans. Amer. Math. Soc.18, no. 3, 331--372, 1917.
A. B. Coble. An application of the form-problems associated with certain Cremona groups to the solution of equations of higher degree.
Trans. Amer. Math. Soc. 9 (1908), no. 4, 396--424.
J. L. Coolidge. A History of Geometrical Methods. Oxford University Press, New York, xviii+451, 1940.
J. L. Coolidge. A treatise on algebraic plane curves. Dover Publications Inc., New York, xxiv+513, 1959.
Y. Cornulier. Nonlinearity of some subgroups of the planar Cremona group. pdf
A. Corti. Factoring birational maps of threefolds after Sarkisov.
J. Algebraic Geom., 4, 2, 223--254, 1995.
B. Costa, T. Dias & R. Gondim. Counting square free Cremona monomial maps. pdf
T. de Fernex. On planar Cremona maps of prime order.
Nagoya Math. J., 174, 1--28, 2004. math.AG/0302175
T. de Fernex & L. Ein. Resolution of indeterminacy of pairs.
Algebraic geometry, 165--177, de Gruyter, Berlin, 2002. pdf
T. Delzant & P. Py. Kähler groups, real hyperbolic spaces and the Cremona group.
Compositio Math. 148, no. 1 (2012), 153--184. arXiv:1012.1585
M. Demazure. Sous-groupes algébriques de rang maximum du groupe de Cremona.
Ann. Sci. École Norm. Sup., (4) 3, 507--588, 1970. pdf
J. Déserti. Quelques propriétés des transformations birationnelles du plan projectif complexe.
Actes du Séminaire de Théorie Spectrale et Géométrie. Vol. 27. Année 2008--2009, 45--100. arXiv:0904.1395
J. Déserti. Sur les automorphismes du groupe de Cremona.
Compos. Math.,142, 6, 1459--1478, 2006. pdf
J. Déserti. Expériences sur certaines transformations birationnelles quadratiques.
Nonlinearity, 21, 6, 1367--1383, 2008. pdf
J. Déserti. Groupe de Cremona et dynamique complexe: une approche de la
conjecture de Zimmer.
Int. Math. Res. Not., Art. ID 71701, 27, 2006. pdf
J. Déserti. Le groupe de Cremona est hopfien.
C. R. Math. Acad. Sci. Paris, 344, 3, 153--156, 2007. math.GR/0611572
J. Déserti. Sur les sous-groupes nilpotents du groupe de Cremona.
Bull. Braz. Math. Soc. (N.S.), 38, 3, 377--388, 2007. math.GR/0606767
J. Déserti. Sur le groupe des automorphismes polynomiaux du plan affine.
J. Algebra, 297, 2, 584--599, 2006. pdf, Erratum
J. Déserti. Some properties of the Cremona group.
Ensaios Mateméticos, 21. Sociedade Brasileira de Matemética, Rio de Janeiro, 2012. ii+188 pp pdf.
J. Déserti & J. Grivaux. Automorphisms of rational surfaces with positive topological entropy.
Indiana Univ. Math. J., 60 No. 5 (2011), 1589-1622 pdf
J. Déserti & F. Han. On cubic birational maps of $\mathbb{P}^3_\mathbb{C}$. pdf
J. Déserti. Some properties of the group of birational maps generated by the automorphisms of $\mathbb{P}^n_{\mathbb{C}}$ and the standard involution.
Math. Z. 281 (2015), no. 3-4, 893--905. pdf
J. Déserti. Jonquières maps and $\mathrm{SL}(2,\mathbb{C})$-cocycles.
J. Mod. Dyn. 10 (2016), 23--32. pdf
J. Diller. Cremona transformations, surface automorphisms and plane cubics. arXiv:0811.3038
J. Diller & J.-L. Lin. Rotation numbers of elements in Thompson's group T. pdf
J. Diller & C. Favre. Dynamics of bimeromorphic maps of surfaces.
Amer. J. Math., 123, 6, 1135--1169, 2001. pdf
J. Diller, D. Jackson & A. Sommese. Invariant curves for birational surface maps.
Trans. Amer. Math. Soc., 359, 6, 2793--2991 (electronic), 2007. math.AG/0505014
I. V. Dolgachev. Luigi Cremona and cubic surfaces. Luigi Cremona (1830--1903).
55--70, Incontr. Studio, 36, Istituto Lombardo di Scienze e Lettere, Milan, 2005. math.AG/0408283
I. V. Dolgachev. Weyl groups and Cremona transformations.
Singularities, Part 1 (Arcata, Calif., 1981), 283--294, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.
I. V. Dolgachev. Polar Cremona transformations. Dedicated to William Fulton on the occasion of his 60th birthday.
Michigan Math. J. 48 (2000), 191--202. math.AG/0005048
I. V. Dolgachev. Topics in Classical Algebraic Geometry,pdf
I. V. Dolgachev & V. A. Iskovskikh. Finite subgroups of the plane Cremona group.
Algebra, Arithmetic, and Geometry: Volume I: In Honor of Y.I. Manin, Progr. Math., 269, 443--548, 2009. math/0610595
I. V. Dolgachev & V. A. Iskovskikh. On elements of prime order in the plane Cremona group over a perfect field.
Int. Math. Res. Not. IMRN 2009, no. 18, 3467Ã3485. arXiv:0707.4305
I. V. Dolgachev. On elements of order ps in the plane Cremona group over a field of characteristic p.
Tr. Mat. Inst. Steklova 264 (2009), Mnogomernaya Algebraicheskaya Geometriya, 55--62; translation in Proc. Steklov Inst. Math. 264 (2009), no. 1, 48--55. arXiv:0811.1390
I. V. Dolgachev. Lectures on Cremona transformations. text
T. Ducat, I. Hedén & S. Zimmermann. The decomposition groups of plane conics and plane rational cubics
Math. Res. Lett. 26 (2019), no. 1, 35--52. pdf
R. Dujardin. Laminar currents and birational dynamics.
Duke Math. J., 131, 2, 219--247, 2006. math.DS/0409557
L. Ein & N. Shepherd-Barron. Some special Cremona transformations.
Amer. J. Math. 111, no. 5, 783--800, 1989.
C. Favre. Points périodiques d'applications birationnelles de P2.
Ann. Inst. Fourier (Grenoble), 48, 4, 999--1023, 1998. pdf
C. Favre. Le groupe de Cremona et ses sous-groupes de type fini.
Séminaire Bourbaki. Volume 2008/2009. Exposés 997--1011. Astérisque No. 332 (2010), Exp. No. 998, vii, 11--43. pdf
C. Favre & J.-L. Lin. Degree growth of rational maps induced from algebraic structures. pdf
G. Fischer. Complex analytic geometry.
Lecture Notes in Mathematics, Vol. 538, Springer-Verlag, Berlin, vii+201, 1976.
J. E. Fornaess & N. Sibony. Dynamics of $\mathbb{P}^2$ (examples).
Laminations and foliations in dynamics, geometry and topology (Stony Brook, NY, 1998), 47--85, Contemp. Math., 269, Amer. Math. Soc., Providence, RI, 2001. pdf
J. E. Fornaess & N. Sibony. Complex dynamics in higher dimension.
Notes partially written by Estela A. Gavosto. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439, Complex potential theory (Montreal, PQ, 1993), 131--186, Kluwer Acad. Publ., Dordrecht, 1994. pdf
J. E. Fornaess & N. Sibony. Complex dynamics in higher dimension. I.
Complex analytic methods in dynamical systems (Rio de Janeiro, 1992), Astérisque, 222, 5, 201--231, 1994. pdf
J. E. Fornaess & N. Sibony. Complex dynamics in higher dimension. II.
Modern methods in complex analysis (Princeton, NJ, 1992), Ann. of Math. Stud., 137, 135--182, Princeton Univ. Press, Princeton, NJ, 1995. pdf
S. Friedland & J. Milnor. Dynamical properties of plane polynomial automorphisms.
Ergodic Theory Dynam. Systems, 9, 1989, 1, 67--99. pdf
J.-P. Furter. Polynomial composition rigidity and plane polynomial automorphisms..
J. Lond. Math. Soc. (2) 91 (2015), no. 1, 180--202. pdf
J.-P. Furter & S. Lamy. Normal subgroup generated by a plane polynomial automorphism.
Transform. Groups 15 (2010), no. 3, 577--610. pdf
F. Galuppi & M. Mella. Identifiability of homogeneous polynomials and Cremona transformations. pdf
M. Gizatullin. Defining relations for the Cremona group of the plane.
Izv. Akad. Nauk SSSR Ser. Mat., 46, 5, 909--970, 1982. pdf
M. Gizatullin. Rational G-surfaces.
Izv. Akad. Nauk SSSR Ser. Mat., 44, 1, 110--144, 1980.
pdf
M. Gizatullin. On some tensor representations of the Cremona group of the projective plane.
New trends in algebraic geometry (Warwick, 1996), 111--150, London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999.
pdf
M. Gizatullin. The Decomposition, Inertia and Ramification Groups in Birational Geometry.
Algebraic geometry and its applications (Yaroslavl', 1992), 39--45, Aspects Math., E25,
Vieweg, Braunschweig, 1994. pdf
L. Godeaux. Les transformations birationnelles du plan.
Mémor. Sci. Math., no. 122, 2nd ed, Gauthier-Villars, Paris, 70, 1953.
G. Gonzalez-Sprinberg & I. Pan. On characteristic classes of determinantal Cremona transformations.
Math. Ann. 335, no. 2, 479--487, 2006. math.AG/0507353
P. Griffiths & J. Harris. Principles of algebraic geometry.
Wiley Classics Library, Reprint of the 1978 original,
John Wiley & Sons Inc., New York, xiv+813, 1994.
A. Guillot. Un théorème de point fixe pour les endomorphismes de
l'espace projectif avec des applications aux feuilletages
algébriques.
Bull. Braz. Math. Soc. (N.S.), 35, 3, 345--362, 2004. pdf
B. Harbourne. Rational surfaces with infinite automorphism group and no antipluricanonical curve.
Proceedings of the American Mathematical Society, 99, 3, 1987. pdf
S. H. Hassanzadeh & A. Simis. Birational maps with arithmetically Cohen-Macaulay graphs pdf
I. Hedén & S. Zimmermann. The decomposition group of a line in the plane pdf
A. Hirschowitz. Le groupe de Cremona d'après Demazure.
Séminaire Bourbaki, 2ème année (1971/1972), Exp. No. 413, pp. 261--276. Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973.
H. P. Hudson. Cremona Transformations in Plane and Space.
Cambridge University Press, 1927.
H. Hudson. Curves of simple contact on algebraic surfaces.
Math. Ann. 73 (1912), no. 1, 73--85. pdf
H. Hudson. Curves of Contact of any Order on Algebraic Surfaces.
Proc. London Math. Soc. S2-11 no. 1, 398. pdf
H. Hudson. Incidence Relations for Cremona Space Transformations.
J. London Math. Soc. S1-3 no. 1, 3. pdf
H. Hudson. Incidence Relations for Cremona Space Transformations, addendum.
Proc. London Math. Soc. S2-26 no. 1, 453. pdf
H. Hudson. Linear Dependence of the Schur Quadrics of a Cubic Surface.
J. London Math. Soc. S1-1 no. 3, 146. pdf
H. Hudson. On Cubic Birational Space-Transformations.
Amer. J. Math. 34 (1912), no. 2, 203--210. pdf
H. Hudson. On the 3-3 Birational Transformation in Three Dimensions.
Proc. London Math. Soc. S2-10 no. 1, 15. pdf
H. Hudson. On the 3-3 Birational Transformation in three Dimensions, addendum.
Proc. London Math. Soc. S2-9 no. 1, 51. pdf
H. Hudson. On the Product of Two Quadro-Quadric Space-Transformations.
Amer. J. Math. 35 (1913), no. 2, 183--188. pdf
H. Hudson. Plane Homaloidal Families of General Degree.
Proc. London Math. Soc. S2-22 no. 1, 223. pdf
H. Hudson. The Cremona Transformations of a Certain Plane Sextic.
Proc. London Math. Soc. S2-15 no. 1, 385. pdf
V. A. Iskovskih. Minimal models of rational surfaces over arbitrary fields.
Izv. Akad. Nauk SSSR Ser. Mat., 43, 1, 19--43, 237, 1979.
V. A. Iskovskikh. Proof of a theorem on relations in the two-dimensional
Cremona group.
Uspekhi Mat. Nauk, 40, 5(245), 255--256, 1985.
V. A. Iskovskikh. Generators and relations in a two-dimensional Cremona group.
Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 5, 43--48, 1983.
V. A. Iskovskih. Generators in the two-dimensional Cremona group over an unclosed field.
Nova J. Algebra Geom. 1, no. 2, 165--183, 1992.
V. A. Iskovskikh. On finite subgroups of the Cremona group.
Vietnam J. Math. 33, Special Issue, 61--80, 2005.
V. A. Iskovskikh. Generators of the two-dimensional Cremona group over a nonclosed field.
Trudy Mat. Inst. Steklov. 200, 157--170, 1991; translation inProc. Steklov Inst. Math., no. 2 (200), 173--188, 1993. pdf
V. A. Iskovskikh & S. L. Tregub. Relations in the two-dimensional Cremona group over a nonclosed field.
Trudy Mat. Inst. Steklov. 207, 123--152, 1994; translation in Proc. Steklov Inst. Math., no. 6 (207), 111--135, 1995.
V. A. Iskovskikh, F. K. Kabdykairov & S. L. Tregub. Relations in a two-dimensional Cremona group over a perfect field.
Izv. Ross. Akad. Nauk Ser. Mat. 57, no. 3, 3--69, 1993; translation in Russian Acad. Sci. Izv. Math. 42, no. 3, 427--478, 1994.
D. Jackson. Invariant curves for birational maps. Ph.D. thesis, University of Notre Dame, 2005.
P. M. Johnson. Inverses of monomial Cremona maps. arXiv:1105.1188
H. W. E. Jung. Zusammensetzung von Cremonatransformationen der Ebene
aus quadratischen Transformationene. J. Reine Angew. Math., 180, 97--109, 1939.
H. W. E. Jung. Über ganze birationale Transformationen der Ebene.
J. Reine Angew. Math., 184, 161--174, 1942.
S. Kantor. Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene.
Mayer & Mullen, Berlin, 1895.
S. Katz. Recent Work on Cremona transformations. pdf
F. Klein. A Comparative Review Of Recent Researches In Geometry. pdf
J. Kollár & F. Mangolte. Cremona transformations and diffeomorphisms of surfaces. arXiv:0809.3720
H. Kraft & I. Stampfli. On Automorphisms of the Affine Cremona Group.
Ann. Inst. Fourier, 63, 3, 1137--1148, 2013. pdf
H. Kraft, A. Regata & I. Van Santen. Is the affine space determined by its automorphism group ? pdf
S. Lamy. L'alternative de Tits pour Aut[C2].
J. Algebra, 239, 2, 413--437, 2001. pdf
S. Lamy. Une preuve géométrique du théorème de Jung.
Enseign. Math. (2), 48, 3-4, 291--315, 2002. pdf french,pdf english
S. Lamy. Relations dans le groupe de Cremona, d'après Iskovskikh. pdf
S. Lamy. Combinatorics of the tame automorphism group.
À paraître aux Annales de la Faculté des Sciences de Toulouse. pdf
S. Lamy & P. Przytycki. Acylindrical Hyperbolicity of the three-dimensional tame automorphism group. pdf
S. Lamy & S. Zimmermann. Signature morphisms from the Cremona group over a non-closed field. pdf
J. Lesieutre. Some constraints on positive entropy automorphisms of smooth threefolds. pdf
J. Lesieutre. Derived-equivalent rational threefolds. pdf
A. Liendo, A. Regeta & C. Urech. Characterization of affine toric varieties by their automorphism groups.. pdf
A. Lonjou. Non simplicité du groupe de Cremona sur tout corps.
Ann. Inst. Fourier (Grenoble) 66 (2016), no. 5, 2021--2046. pdf
A. Lonjou. Pavage de Voronoi associé au groupe de Cremona. pdf
A. Lonjou. Graphes associés au groupe de Cremona. pdf
G. Loria. L'oeuvre mathématique d'Ernest de Jonquières.
Bibliotheca Mathematica, 3, 276--322, 1902.
G. Loria. Luigi Cremona et son oeuvre mathématique.
Bibliotheca Mathematica, 3, 125--195, 1904.
G. Loria. Sulla classificazione delle trasformazioni razionali dello spazio, in particulare sulle trasformazioni di genere zero. pdf
J.-L. Lin. Algebraic stability and degree growth of monomial maps and polynomial maps.
Math. Z. 271 (2012), no. 1-2, 293--311. pdf
J.-L. Lin. Pulling Back Cohomology Classes and Dynamical Degrees Of Monomial Maps.
Bull. Soc. Math. France 140 (2012), no. 4, 533--549 (2013). pdf
J.-L. Lin. On Degree Growth and Stabilization of Three Dimensional Monomial Maps.
Michigan Math. J. 62 (2013), no. 3, 567--579. pdf
J.-L. Lin & C.-H. Wang. Canonical Height Functions For Monomial Maps.
Int. J. Number Theory 9 (2013), no. 7, 1821--1840. pdf
J.-L. Lin & E. Wulcan. Stabilization of monomial maps in higher codimension.
Ann. Inst. Fourier (Grenoble) 64 (2014), no. 5, 2127--2146. pdf
J. Maher & G. Tiozzo. Random walks, WPD actions, and the Cremona group. pdf
M. Manes & J. Silverman. A classification of degree $2$ semi-stable rational maps $\mathbb{P}^2\to\mathbb{P}^2$ with large finite dynamical automorphism group. pdf
Ju. I. Manin. Rational surfaces over perfect fields. II.
Mat. Sb. (N.S.), 72 (114), 161--192, 1967.
Yu. I. Manin. Cubic forms.
North-Holland Mathematical Library, 4, Second edition,
Amsterdam, x+326, 1986.
Ju. I. Manin. Regular elements in the Cremona group.
Mat. Zametki, 5, 145--148, 1969.
M. Manjarin. Flows of birational quadratic transformations in $\mathbb{P}^3$. pdf
K. Matsuki. Introduction to the Mori program.
Universitext, Springer-Verlag, New York, xxiv+478, 2002.
M. Menghini. Notes on the correspondence between Luigi Cremona and Max Noether.
Historia Mathematica (13), 4, 341--351, 1986. pdf
M. Nagata. On rational surfaces, II.
Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 1960/1961 271--293.
M. Noether. Ueber die auf Ebenen eindeutig abbildbaren algebraischen Flächen.
Göttigen Nachr., 1--6, 1869.
M. Noether, Ueber Flächen, welche Schaaren rationaler Curven besitzen.
Math. Ann., 3(2), 161--227, 1870.
M. Noether. Zur Theorie der eindentigen Ebenentrasformationen.
Math. Ann., 5(4), 635--639, 1872.
K. Oguiso. Some aspects of explicit birational geometry inspired by complex dynamics. pdf
K. Oguiso. Pisot units Salem numbers and higher dimensional projective manifolds with primitive automorphisms of positive entropy. pdf
I. Pan. Sur le degré dynamique des transformations de Cremona du
plan qui stabilisent une courbe irrationnelle non-elliptique.
C. R. Math. Acad. Sci. Paris, 341, 7, 439--443, 2005. pdf
I. Pan. Sur le sous-groupe de décomposition d'une courbe
irrationnelle dans le groupe de Cremona du plan.
Michigan Math. J., 55, 2, 285--298, 2007. pdf
I. Pan. Une remarque sur la génération du groupe de Cremona.
Bol. Soc. Brasil. Mat. (N.S.), 30, 1, 95--98, 1999. pdf
I. Pan. Les transformations de Cremona stellaires.
Proc. Amer. Math. Soc. 129, no. 5, 1257--1262 (electronic), 2001. pdf
I. Pan. Sur le multidegré des transformations de Cremona.
C. R. Acad. Sci. Paris Sér. I Math., 330, no. 4, 297--300, 2000. pdf
I. Pan. Sur les transformations de Cremona de bidegré (3,3).
Enseign. Math. (2) 43, no. 3-4, 285--297, 1997.
I. Pan. On Cremona Transformations of $\mathbb{P}^3$ which factorize in a minimal form.
Rev. Un. Mat. Argentina 54 (2013), no. 2, 37--58. arXiv:1104.4986
I. Pan & F. Russo. Cremona transformations and special double structures.
Manuscripta Math. 117, no. 4, 491--510, 2005. pdf
I. Pan, F. Ronga & T. Vust. Transformations birationnelles quadratiques de l'espace projectif complexe à trois dimensions.
Ann. Inst. Fourier (Grenoble) 51 (2001), no. 5, 1153--1187. pdf
I. Pan & A. Simis. Cremona maps of de Jonquières type.
Canad. J. Math. 67 (2015), no. 4, 923--941. pdf
L. Pirio & F. Russo. Quadro-quadric Cremona transformations in low dimensions via the JC-correspondence.
Ann. Inst. Fourier (Grenoble) 64 (2014), no. 1, 71--111. pdf
L. Pirio & F. Russo. Extremal varieties 3-rationally connected by cubics, quadro-quadric Cremona transformations
and rank 3 Jordan algebras. pdf
. V. L. Popov. Some subgroups of the Cremona groups arXiv:1110.2410
Y. Prokhorov. p-elementary subgroups of the Cremona group of rank 3
Classification of algebraic varieties, 327--338, EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich, 2011. pdf
Y. Prokhorov. 2-elementary subgroups of the space Cremona group.
Automorphisms in birational and affine geometry, 215--229, Springer Proc. Math. Stat., 79, Springer, Cham, 2014. pdf
Y. Prokhorov. On stable conjugacy of finite subgroups of the plane Cremona Cremona group, II.
Michigan Math. J. 64 (2015), no. 2, 293--318. pdf
Y. Prokhorov. On stable conjugacy of finite subgroups of the plane Cremona Cremona group, I.
Cent. Eur. J. Math. 11 (2013), no. 12, 2099--2105. pdf
Y. Prokhorov & C. Shramov. Jordan property for groups of birational selfmaps.
Compos. Math. 150 (2014), no. 12, 2054--2072. pdf
Y. Prokhorov & C. Shramov. Jordan constant for Cremona group of rank 3. pdf
Y. Prokhorov & C. Shramov. p-subgroups in the space Cremona group. pdf
Y. Prokhorov & C. Shramov. Finite groups of birational selfmaps of threefolds. pdf
Z. Reichstein. The Jordan property of Cremona groups and essential dimension. pdf
M. Robayo & S. Zimmermann. Infinite algebraic subgroups of the real Cremona group.
Osaka J. Math. 55 (2018), no. 4, 681--712. pdf
R. Roeder. The action on cohomology by compositions of rational maps. pdf
F. Ronga & T. Vust. Birational diffeomorphisms of the real projective plane.
Comment. Math. Helv., 80, 3, 517--540, 2005.
J. Schneider. Relations in the Cremona group over perfect fields. pdf
J. G. Semple & L. Roth. Introduction to algebraic geometry.
Oxford Science Publications, Reprint of the 1949 original, The Clarendon Press Oxford University Press, New York, xviii+454, 1985.
C. Segre.
Un'osservazione relativa alla riducibilità delle trasformazioni cremoniane e dei sistemi lineari di cuve piane per mezzo di trasformazioni quadratiche.
Atti. della R. Accad. delle Scienze di Torino, 26, 377--383, 1901.
C. Segre. La trasformazioni generatrici del gruppo cremoniano nel piano.
Accad. delle Scienze di Torino, 36, 872, 1871.
J.-P. Serre. Le groupe de Cremona et ses sous-groupes finis.
Séminaire Bourbaki. Volume 2008/2009. Exposés 997--1011. Astérisque No. 332 (2010), Exp. No. 1000, vii, 75--100. pdf
J.-P. Serre. A Minkowski-style bound for the order of the finite subgroups of the Cremona group of rank 2 over an arbitrary field. pdf
N. I. Shepherd-Barron. Some effectivity questions for plane Cremona transformations. pdf
A. Simis & R. H. Villarreal . Combinatorics of Cremona monomial maps. arXiv:0904.4065
V. Snyder. Review on Cremona Transformations in Plane and Space by H. Hudson.
Amer. Math. Monthly 34 (1927), no. 9, 487--488. pdf
C. P. Sousley. Invariants and Covariants of the Cremona Cubic Surface.
Amer. J. Math. 39 (1917), no. 2, 135--146. pdf
G. Staglianò. Special cubic Cremona transformations of $\mathbb{P}^6$ and $\mathbb{P}^7$. pdf
E. Study. Ueber die Cremona'sche Charakteristikenformel.
Math. Ann. 27 (1886), no. 1, 102--105. pdf
R. Sturm. Beispiele zu den Cremona'schen ebenen Transformationen.
Math. Ann. 26 (1886), no. 2, 304--308. pdf
M. E. Taylor. A Determination of the Types of Planar Cremona Transformations with not More than 9 F-Points.
Amer. J. Math. 54 (1932), no. 1, 123--128. pdf
J. Tits. The Cremona plane.
Cours du coll&eagrave; de France donné è l'Université libre de Bruxelles en mars 1999. pdf
C. C. Torrance. On Plane Cremona Triadic Characteristics.
Amer. J. Math. 53 (1931), no. 4, 911--919. pdf
T. T. Truong. Degree complexity of a family of birational maps: II. Exceptional cases. pdf
T.T. Truong. On automorphisms of blowups of $\mathbb{P}^3$. arXiv:1202.4224
T. Uehara. Rational Surface Automorphisms with Positive Entropy. pdf
V. I. Tsygankov. The finite nonsolvable subgroups in the plane Cremona group. arXiv:1105.3156
H. Umemura. Sur les sous-groupes algébriques primitifs du groupe de Cremona à trois variables.
Nagoya Math. J., 79 47--67, 1980. pdf
H. Umemura. On the maximal connected algebraic subgroups of the Cremona group. I.
Nagoya Math. J. 88, 213--246, 1982. pdf
H. Umemura. On the maximal connected algebraic subgroups of the Cremona group. II.
Algebraic groups and related topics (Kyoto/Nagoya, 1983), 349--436, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985. pdf
H. Umemura. Maximal algebraic subgroups of the Cremona group of three variables. Imprimitive algebraic subgroups of exceptional type.
Nagoya Math. J. 87, 59--78, 1982.
C. Urech. On homomorphisms between Cremona groups.
Ann. Inst. Fourier (Grenoble) 68 (2018), no. 1, 53--100. pdf
C. Urech. Remarks on the degree growth of birational transformations.
Math. Res. Lett. 25 (2018), no. 1, 291--308. pdf
C. Urech. Simple groups of birational transformations in dimension two. pdf
C. Urech. Subgroups of elliptic elements of the Cremona group. pdf
C. Urech, S. Zimmermann. A new presentation of the plane Cremona group.
Proc. Amer. Math. Soc. 147 (2019), no. 7, 2741--2755. pdf
C. Urech, S. Zimmermann. Continuous automorphisms of Cremona groups. pdf
A. Usnich. Symplectic automorphisms of CP^2 and the Thompson group T. pdf
A. Verra. Lectures on Cremona transformations.
M. L. Vest. Cremona transformations associated with the chords of a twisted cubic.
Duke Math. J. 19, (1952). 397--408. pdf
T. Viola. Sui diagrammi reciproci del Cremona.
Ann. Mat. Pura Appl. 10 (1932), no. 1, 167--172. pdf
H. S.Wall. Continued fractions and cross-ratio groups of Cremona transformations.
Bull. Amer. Math. Soc. 40 (1934), no. 8, 587--592. pdf
H. S.White. Book review "Opere matematiche di Luigi Cremona".
Bull. Amer. Math. Soc. 24 (1918), no. 5, 238--243. pdf
A. Wiman. Zur theorie der endlichen gruppen von birazionalen transformationen in der ebene. Math. Ann., 4, 1987.
D. Wright. Two-dimensional Cremona groups acting on simplicial
complexes. Trans. Amer. Math. Soc., 331, 1, 281--300, 1992. pdf
D. Wright. Abelian subgroups of Aut_k(k[X,Y]) and applications to actions on the affine plane. Illinois J. Math. 23 (1979), no. 4, 579--634. pdf
D. Wright. The generalized amalgamated product structure of the tame automorphism group in dimension three. Transform. Groups 20 (2015), no. 1, 291--304. pdf
J. Xie. Periodic points of birational maps on the projective plane. arXiv:1106.1825
E. Yasinsky. Subgroups of odd order in the real plane Cremona group. pdf
E. Yasinsky. The Jordan constant for Cremona group of rank 2. pdf
S. Zhao. Centralizers of elements of infinite order in plane Cremona groups. pdf
S. Zimmermann. The Cremona group is compactly presentable.
J. Lond. Math. Soc. (2) 93 (2016), no. 1, 25--46. pdf
S. Zimmermann. The abelianisation of the Real Cremona group.
Duke Math. J. 167 (2018), no. 2, 211--267. pdf
S. Zimmermann. The real plane Cremona group is a non-trivial amalgam. pdf