Ces notes sont issues d’un mini-cours donné à la cinquième École d’Hiver KAWA du 24 au 29 Mars 2014, au CIRM à Marseille. Elles donnent une introduction à l’hyperbolicité des variétés algébriques complexes à savoir la géométrie des courbes entières, ainsi qu’une description de certains développements récents.
These lecture notes are based on a mini-course given at the fifth KAWA Winter School on March 24-29, 2014 at CIRM, Marseille. They provide an introduction to hyperbolicity of complex algebraic varieties namely the geometry of entire curves, and a description of some recent developments.
@article{AFST_2018_6_27_2_421_0, author = {Rousseau, Erwan}, title = {KAWA lecture notes on complex hyperbolic geometry}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {421--443}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 27}, number = {2}, year = {2018}, doi = {10.5802/afst.1574}, mrnumber = {3831029}, zbl = {1398.32032}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1574/} }
TY - JOUR AU - Rousseau, Erwan TI - KAWA lecture notes on complex hyperbolic geometry JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2018 DA - 2018/// SP - 421 EP - 443 VL - Ser. 6, 27 IS - 2 PB - Université Paul Sabatier, Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1574/ UR - https://www.ams.org/mathscinet-getitem?mr=3831029 UR - https://zbmath.org/?q=an%3A1398.32032 UR - https://doi.org/10.5802/afst.1574 DO - 10.5802/afst.1574 LA - en ID - AFST_2018_6_27_2_421_0 ER -
Rousseau, Erwan. KAWA lecture notes on complex hyperbolic geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 2, pp. 421-443. doi : 10.5802/afst.1574. http://www.numdam.org/articles/10.5802/afst.1574/
[1] Quotients of products of curves, new surfaces with and their fundamental groups, Am. J. Math., Volume 134 (2012) no. 4, pp. 993-1049 | Article | MR 2956256 | Zbl 1258.14043
[2] Families of curves on a surface of general type, Dokl. Akad. Nauk SSSR, Volume 236 (1977) no. 5, pp. 1041-1044 | MR 0457450 | Zbl 0415.14013
[3] On the hyperbolicity of general hypersurfaces, Publ. Math., Inst. Hautes Étud. Sci., Volume 126 (2017), pp. 1-34 | Article | MR 3735863 | Zbl 06827883
[4] Complete intersection varieties with ample cotangent bundles, Invent. Math., Volume 212 (2018) no. 3, pp. 913-940 | Article | MR 3802300 | Zbl 1401.14203
[5] Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 5, pp. 569-594 | Article | Numdam | MR 1474805 | Zbl 0893.32019
[6] Courbes entières et feuilletages holomorphes, Enseign. Math., Volume 45 (1999) no. 1-2, pp. 195-216 | MR 1703368 | Zbl 1004.32011
[7] Birational geometry of foliations, Publicações Matemáticas do IMPA, Instituto de Matemática Pura e Aplicada, 2004, iv+138 pages | MR 2114696 | Zbl 1082.32022
[8] Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials, Algebraic geometry (Santa Cruz 1995) (Proceedings of Symposia in Pure Mathematics), Volume 62, American Mathematical Society, 1997, pp. 285-360 | Article | MR MR1492539 | Zbl 0919.32014
[9] Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q., Volume 7 (2011) no. 4, pp. 1165-1207 | Article | MR 2918158 | Zbl 1316.32014
[10] Towards the Green-Griffiths-Lang conjecture (2014) (https://arxiv.org/abs/1412.2986) | Zbl 1327.14048
[11] Effectivity in the Hyperbolicity-related problem (2016) (https://arxiv.org/abs/1606.03831)
[12] Effective algebraic degeneracy, Invent. Math., Volume 180 (2010) no. 1, pp. 161-223 | Article | MR 2593279 | Zbl 1192.32014
[13] The exceptional set and the Green-Griffiths locus do not always coincide, Enseign. Math., Volume 61 (2015) no. 3-4, pp. 417-452 | Article | MR 3539844 | Zbl 1359.32020
[14] Sur le lemme de Brody, Invent. Math., Volume 173 (2008) no. 2, pp. 305-314 | Article | MR 2415309 | Zbl 1155.32017
[15] Ein Verschwindungssatz für automorphe Formen zur Siegelschen Modulgruppe, Math. Z., Volume 165 (1979) no. 1, pp. 11-18 | Article | MR 521517 | Zbl 0393.10027
[16] Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979 (Berkeley 1979), Springer, 1980, pp. 41-74 | Article | MR MR609557 | Zbl 0508.32010
[17] Hypersurfaces solutions d’une équation de Pfaff analytique, Math. Ann., Volume 232 (1978) no. 3, pp. 239-245 | Article | MR 0481129 | Zbl 0354.34007
[18] Singularities of pairs, Algebraic geometry (Santa Cruz 1995) (Proceedings of Symposia in Pure Mathematics), Volume 62, American Mathematical Society, 1997, pp. 221-287 | Article | MR 1492525 | Zbl 0905.14002
[19] Hyperbolic and Diophantine analysis, Bull. Am. Math. Soc., Volume 14 (1986) no. 2, pp. 159-205 | Article | MR 828820 | Zbl 0602.14019
[20] Holomorphic curves in surfaces of general type, Proc. Nat. Acad. Sci. U.S.A., Volume 87 (1990) no. 1, pp. 80-82 | Article | MR 1031949 | Zbl 0702.32015
[21] Diophantine approximations and foliations, Publ. Math., Inst. Hautes Étud. Sci., Volume 87 (1998), pp. 121-174 | Article | MR MR1659270 | Zbl 1006.32020
[22] Canonical models of foliations, Pure Appl. Math. Q., Volume 4 (2008) no. 3, pp. 877-1012 | Article | MR 2435846 | Zbl 1166.14010
[23] Metric rigidity theorems on Hermitian locally symmetric manifolds, Series in Pure Mathematics, 6, World Scientific, 1989, xiv+278 pages | MR 1081948 | Zbl 0912.32026
[24] Hirzebruch’s proportionality theorem in the noncompact case, Invent. Math., Volume 42 (1977), pp. 239-272 | Article | MR 471627 | Zbl 0365.14012
[25] The nonexistence of certain level structures on abelian varieties over complex function fields, Ann. Math., Volume 129 (1989) no. 1, pp. 161-178 | Article | MR 979604 | Zbl 0675.14018
[26] Hyperbolicity, automorphic forms and Siegel modular varieties, Ann. Sci. Éc. Norm. Supér., Volume 49 (2016) no. 1, pp. 249-255 | Article | MR 3465981 | Zbl 1361.32032
[27] Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, 11, Princeton University Press, 1994, xiv+271 pages (Reprint of the 1971 original) | MR 1291394 | Zbl 0872.11023
[28] On Brody and entire curves, Bull. Soc. Math. Fr., Volume 135 (2007) no. 1, pp. 25-46 | Article | Numdam | MR 2430197 | Zbl 1159.32015
[29] On the ampleness of the cotangent bundles of complete intersections, Invent. Math., Volume 212 (2018) no. 3, pp. 941-996 | MR 3802301 | Zbl 1405.14119
Cité par Sources :