Quelques propriétés des transformations birationnelles du plan projectif complexe, une histoire pour S.

 Access to full text

 Full (PDF)

1. M. Alberich-Carramiñana, Plane Cremona maps, exceptional curves and roots, Trans. Amer. Math. Soc. 357 (2005), 1901-1914 (electronic) Zbl1065.14046MR2115081
2. L. Bayle, A. Beauville, Birational involutions of ${\mathbf{P}}^2$, Asian J. Math. 4 (2000), 11-17 Zbl1055.14012MR1802909
3. A. Beauville, Surfaces algébriques complexes, (1978), Société Mathématique de France, Paris Zbl0394.14014MR485887
4. A. Beauville, $p$-elementary subgroups of the Cremona group, J. Algebra 314 (2007), 553-564 Zbl1126.14017MR2344578
5. A. Beauville, J. Blanc, On Cremona transformations of prime order, C. R. Math. Acad. Sci. Paris 339 (2004), 257-259 Zbl1062.14017MR2092009
6. E. Bedford, K. Kim, Periodicities in linear fractional recurrences : degree growth of birational surface maps, Michigan Math. J. 54 (2006), 647-670 Zbl1171.37023MR2280499
7. E. Bedford, K. Kim, Dynamics of rational surface automorphisms : linear fractional recurrences, J. Geom. Anal. 19 (2009), 553-583 Zbl1185.37128MR2496566
8. E. Bedford, K. Kim, Continuous Families of Rational Surface Automorphisms with Positive Entropy, Math. Ann. 348 (2010), 667-688 Zbl1202.37063MR2677899
9. E. Bertini, Ricerche sulle trasformazioni univoche involutorie nel piano, Annali di Mat. 8 (1877), 244-286 Zbl09.0578.02
10. G. Birkhoff, Lie groups simply isomorphic with no linear group, Bull. Amer. Math. Soc. 42 (1936), 883-888 Zbl62.0442.02MR1563459
11. J. Blanc, The number of conjugacy classes of elements of the Cremona group of some given finite order, Bull. Soc. Math. France 135 (2007), 419-434 Zbl1158.14017MR2430188
12. J. Blanc, Elements and cyclic subgroups of finite order of the Cremona group, (2008) 
13. J. Blanc, On the inertia group of elliptic curves in the Cremona group of the plane, Michigan Math. J. 56 (2008), 315-330 Zbl1156.14011MR2492397
14. J. Blanc, Linearisation of finite abelian subgroups of the Cremona group of the plane, Groups Geom. Dyn. 3 (2009), 215-266 Zbl1170.14009MR2486798
15. J. Blanc, I. Pan, T. Vust, Sur un théorème de Castelnuovo, Bull. Braz. Math. Soc. (N.S.) 39 (2008), 61-80 Zbl1139.14014MR2390684
16. M. Brunella, Birational geometry of foliations, (2004), Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro Zbl1082.32022MR2114696
17. A. Campillo, J. Olivares, Assigned base conditions and geometry of foliations on the projective plane, Singularities—Sapporo 1998 29 (2000), 97-113, Kinokuniya, Tokyo Zbl1083.14032MR1819632
18. S. Cantat, Dynamique des automorphismes des surfaces complexes compactes, (1999) 
19. S. Cantat, Dynamique des automorphismes des surfaces projectives complexes, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), 901-906 Zbl0943.37021MR1689873
20. S. Cantat, Dynamique des automorphismes des surfaces $K3$, Acta Math. 187 (2001), 1-57 Zbl1045.37007MR1864630
21. S. Cantat, Sur les groupes de transformations birationnelles des surfaces, (2006) 
22. S. Cantat, C. Favre, Symétries birationnelles des surfaces feuilletées, J. Reine Angew. Math. 561 (2003), 199-235 Zbl1070.32022MR1998612
23. S. Cantat, S. Lamy, Groupes d’automorphismes polynomiaux du plan, Geom. Dedicata 123 (2006), 201-221 Zbl1115.14055MR2299735
24. S. Cantat, S. Lamy, Normal subgroups in the Cremona group, (2010) Zbl1278.14017
25. G. Castelnuovo, Sulle transformazioni cremoniane del piano, che ammettono una curva fiera, Rend. Accad. Lincei (1892) Zbl24.0577.03
26. G. Castelnuovo, Le trasformationi generatrici del gruppo cremoniano nel piano, Atti della R. Accad. delle Scienze di Torino 36 (1901), 861-874 Zbl32.0675.03
27. D. Cerveau, J. Déserti, Transformations birationnelles de petit degré, (2008) 
28. V. I. Danilov, Non-simplicity of the group of unimodular automorphisms of an affine plane, Mat. Zametki 15 (1974), 289-293 Zbl0295.12102MR357626
29. T. de Fernex, On planar Cremona maps of prime order, Nagoya Math. J. 174 (2004), 1-28 Zbl1062.14019MR2066103
30. J. Déserti, Groupe de Cremona et dynamique complexe : une approche de la conjecture de Zimmer, Int. Math. Res. Not. (2006) Zbl1119.22007MR2233717
31. J. Déserti, Sur le groupe des automorphismes polynomiaux du plan affine, J. Algebra 297 (2006), 584-599 Zbl1096.14046MR2209276
32. J. Déserti, Sur les automorphismes du groupe de Cremona, Compos. Math. 142 (2006), 1459-1478 Zbl1109.14015MR2278755
33. J. Déserti, Le groupe de Cremona est hopfien, C. R. Math. Acad. Sci. Paris 344 (2007), 153-156 Zbl1109.22006MR2292279
34. J. Déserti, Sur les sous-groupes nilpotents du groupe de Cremona, Bull. Braz. Math. Soc. (N.S.) 38 (2007), 377-388 Zbl1222.14028MR2344204
35. J. Déserti, Expériences sur certaines transformations birationnelles quadratiques, Nonlinearity 21 (2008), 1367-1383 Zbl1153.37380MR2422385
36. J. A. Dieudonné, La géométrie des groupes classiques, (1971), Springer-Verlag, Berlin Zbl0221.20056MR310083
37. J. Diller, C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (2001), 1135-1169 Zbl1112.37308MR1867314
38. J. Diller, D. Jackson, A. Sommese, Invariant curves for birational surface maps, Trans. Amer. Math. Soc. 359 (2007), 2793-2991 (electronic) Zbl1115.14007MR2286065
39. I. V. Dolgachev, V. A. Iskovskikh, Finite subgroups of the plane Cremona group, Algebra, arithmetic, and geometry : in honor of Yu. I. Manin. Vol. I 269 (2009), 443-548, Birkhäuser Boston Inc., Boston, MA Zbl1219.14015MR2641179
40. C. Favre, Le groupe de Cremona et ses sous-groupes de type fini 
41. G. Fischer, Complex analytic geometry, (1976), Springer-Verlag, Berlin Zbl0343.32002MR430286
42. S. Friedland, J. Milnor, Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dynam. Systems 9 (1989), 67-99 Zbl0651.58027MR991490
43. J.-P. Furter, S. Lamy, Normal subgroup generated by a plane polynomial automorphism, (2009) Zbl1226.14080MR2718938
44. É. Ghys, Groups acting on the circle, Enseign. Math. (2) 47 (2001), 329-407 Zbl1044.37033MR1876932
45. M. Gizatullin, On some tensor representations of the Cremona group of the projective plane, New trends in algebraic geometry (Warwick, 1996) 264 (1999), 111-150, Cambridge Univ. Press, Cambridge Zbl0980.14011MR1714823
46. M. H. Gizatullin, Rational $G$-surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 110-144, 239 Zbl0428.14022MR563788
47. M. H. Gizatullin, The decomposition, inertia and ramification groups in birational geometry, Algebraic geometry and its applications (Yaroslavl, 1992) (1994), 39-45, Vieweg, Braunschweig Zbl0834.14006MR1282018
48. M. Kh. Gizatullin, Defining relations for the Cremona group of the plane, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 909-970, 1134 Zbl0509.14011MR675525
49. X. Gómez-Mont, G. Kempf, Stability of meromorphic vector fields in projective spaces, Comment. Math. Helv. 64 (1989), 462-473 Zbl0709.14008MR998859
50. M. J. Greenberg, Euclidean and non-Euclidean geometries, (1993), W. H. Freeman and Company, New York Zbl1127.51001MR1261866
51. V. A. Iskovskikh, Minimal models of rational surfaces over arbitrary fields, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 19-43, 237 Zbl0412.14012MR525940
52. V. A. Iskovskikh, Proof of a theorem on relations in the two-dimensional Cremona group, Uspekhi Mat. Nauk 40 (1985), 255-256 Zbl0613.14012MR810819
53. H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161-174 Zbl0027.08503MR8915
54. S. Kantor, Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene, Mayer & Müller, Berlin (1895) Zbl26.0770.03
55. M. Koitabashi, Automorphism groups of generic rational surfaces, J. Algebra 116 (1988), 130-142 Zbl0663.14033MR944150
56. J. Kollár, F. Mangolte, Cremona transformations and diffeomorphisms of surfaces, (2008) Zbl1188.14008MR2531367
57. S. Lamy, L’alternative de Tits pour $\mathrm{Aut}\left[{ℂ}^2\right]$, J. Algebra 239 (2001), 413-437 Zbl1040.37031MR1832900
58. S Lamy, Une preuve géométrique du théorème de Jung, Enseign. Math. (2) 48 (2002), 291-315 Zbl1044.14035MR1955604
59. Ju. I. Manin, Rational surfaces over perfect fields. II, Mat. Sb. (N.S.) 72 (114) (1967), 161-192 Zbl0182.23701MR225781
60. Yu. I. Manin, Cubic forms, 4 (1986), North-Holland Publishing Co., Amsterdam Zbl0277.14014MR833513
61. C. T. McMullen, Dynamics on blowups of the projective plane, Publ. Math. Inst. Hautes Études Sci. (2007), 49-89 Zbl1143.37033MR2354205
62. M. McQuillan, Diophantine approximations and foliations, Inst. Hautes Études Sci. Publ. Math. (1998), 121-174 Zbl1006.32020MR1659270
63. L. G. Mendes, Kodaira dimension of holomorphic singular foliations, Bol. Soc. Brasil. Mat. (N.S.) 31 (2000), 127-143 Zbl0979.32017MR1785264
64. M. Noether, Ueber die auf Ebenen eindeutig abbildbaren algebraischen Flächen, Göttigen Nachr. (1869), 1-6 
65. M. Noether, Ueber Flächen, welche Schaaren rationaler Curven besitzen, Math. Ann. 3(2) (1870), 161-227 MR1509694
66. M. Noether, Zur Theorie der eindentigen Ebenentrasformationen, Math. Ann. 5(4) (1872), 635-639 MR1509801
67. I. Pan, Une remarque sur la génération du groupe de Cremona, Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), 95-98 Zbl0972.14006MR1686984
68. I. Pan, Sur le sous-groupe de décomposition d’une courbe irrationnelle dans le groupe de Cremona du plan, Michigan Math. J. 55 (2007), 285-298 Zbl1144.14010MR2369937
69. F. Ronga, T. Vust, Birational diffeomorphisms of the real projective plane, Comment. Math. Helv. 80 (2005), 517-540 Zbl1080.14020MR2165201
70. K. Saito, On a generalization of de-Rham lemma, Ann. Inst. Fourier (Grenoble) 26 (1976), vii, 165-170 Zbl0338.13009MR413155
71. P. E. Schupp, Small cancellation theory over free products with amalgamation, Math. Ann. 193 (1971), 255-264 Zbl0209.05204MR291298
72. J. G. Semple, L. Roth, Introduction to algebraic geometry, (1985), The Clarendon Press Oxford University Press, New York Zbl0576.14001MR814690
73. J.-P. Serre, Arbres, amalgames, ${\mathrm{SL}}_2$, (1977), Société Mathématique de France, Paris Zbl0369.20013MR476875
74. R. Steinberg, Some consequences of the elementary relations in ${\mathrm{SL}}_n$, Finite groups—coming of age (Montreal, Que., 1982) 45 (1985), 335-350, Amer. Math. Soc., Providence, RI Zbl0579.20038MR822247
75. J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250-270 Zbl0236.20032MR286898
76. A. Wiman, Zur theorie der endlichen gruppen von birazionalen transformationen in der ebene, Math. Ann. 48 (1896), 195-240 Zbl30.0600.01MR1510931
77. D. Wright, Two-dimensional Cremona groups acting on simplicial complexes, Trans. Amer. Math. Soc. 331 (1992), 281-300 Zbl0767.14006MR1038019
78. R. J. Zimmer, Actions of semisimple groups and discrete subgroups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) (1987), 1247-1258, Amer. Math. Soc., Providence, RI Zbl0671.57028MR934329