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KAWA lecture notes on complex hyperbolic geometry
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 2, pp. 421-443.

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.

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.

Published online:
DOI: 10.5802/afst.1574
Erwan Rousseau 1

1 Institut Universitaire de France & Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Erwan Rousseau. KAWA lecture notes on complex hyperbolic geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 2, pp. 421-443. doi : 10.5802/afst.1574. https://afst.centre-mersenne.org/articles/10.5802/afst.1574/

[1] Ingrid Bauer; Fabrizio Catanese; Fritz Grunewald; Roberto Pignatelli Quotients of products of curves, new surfaces with p g =0 and their fundamental groups, Am. J. Math., Volume 134 (2012) no. 4, pp. 993-1049 | DOI | MR | Zbl

[2] Fedor A. Bogomolov Families of curves on a surface of general type, Dokl. Akad. Nauk SSSR, Volume 236 (1977) no. 5, pp. 1041-1044 | MR | Zbl

[3] Damian Brotbek On the hyperbolicity of general hypersurfaces, Publ. Math., Inst. Hautes Étud. Sci., Volume 126 (2017), pp. 1-34 | DOI | MR | Zbl

[4] Damian Brotbek; Lionel Darondeau Complete intersection varieties with ample cotangent bundles, Invent. Math., Volume 212 (2018) no. 3, pp. 913-940 | DOI | MR | Zbl

[5] Marco Brunella Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 5, pp. 569-594 | DOI | Numdam | MR | Zbl

[6] Marco Brunella Courbes entières et feuilletages holomorphes, Enseign. Math., Volume 45 (1999) no. 1-2, pp. 195-216 | MR | Zbl

[7] Marco Brunella Birational geometry of foliations, Publicações Matemáticas do IMPA, Instituto de Matemática Pura e Aplicada, 2004, iv+138 pages | MR | Zbl

[8] Jean-Pierre Demailly 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 | DOI | MR | Zbl

[9] Jean-Pierre Demailly Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q., Volume 7 (2011) no. 4, pp. 1165-1207 | DOI | MR | Zbl

[10] Jean-Pierre Demailly Towards the Green-Griffiths-Lang conjecture (2014) (https://arxiv.org/abs/1412.2986) | Zbl

[11] Ya Deng Effectivity in the Hyperbolicity-related problem (2016) (https://arxiv.org/abs/1606.03831)

[12] Simone Diverio; Joël Merker; Erwan Rousseau Effective algebraic degeneracy, Invent. Math., Volume 180 (2010) no. 1, pp. 161-223 | DOI | MR | Zbl

[13] Simone Diverio; Erwan Rousseau The exceptional set and the Green-Griffiths locus do not always coincide, Enseign. Math., Volume 61 (2015) no. 3-4, pp. 417-452 | DOI | MR | Zbl

[14] Julien Duval Sur le lemme de Brody, Invent. Math., Volume 173 (2008) no. 2, pp. 305-314 | DOI | MR | Zbl

[15] Eberhard Freitag Ein Verschwindungssatz für automorphe Formen zur Siegelschen Modulgruppe, Math. Z., Volume 165 (1979) no. 1, pp. 11-18 | DOI | MR | Zbl

[16] Mark Green; Phillip Griffiths Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979 (Berkeley 1979), Springer, 1980, pp. 41-74 | DOI | MR | Zbl

[17] Jean-Pierre Jouanolou Hypersurfaces solutions d’une équation de Pfaff analytique, Math. Ann., Volume 232 (1978) no. 3, pp. 239-245 | DOI | MR | Zbl

[18] János Kollár Singularities of pairs, Algebraic geometry (Santa Cruz 1995) (Proceedings of Symposia in Pure Mathematics), Volume 62, American Mathematical Society, 1997, pp. 221-287 | DOI | MR | Zbl

[19] Serge Lang Hyperbolic and Diophantine analysis, Bull. Am. Math. Soc., Volume 14 (1986) no. 2, pp. 159-205 | DOI | MR | Zbl

[20] Steven Shin-Yi Lu; Shing-Tung Yau Holomorphic curves in surfaces of general type, Proc. Nat. Acad. Sci. U.S.A., Volume 87 (1990) no. 1, pp. 80-82 | DOI | MR | Zbl

[21] Michael McQuillan Diophantine approximations and foliations, Publ. Math., Inst. Hautes Étud. Sci., Volume 87 (1998), pp. 121-174 | DOI | MR | Zbl

[22] Michael McQuillan Canonical models of foliations, Pure Appl. Math. Q., Volume 4 (2008) no. 3, pp. 877-1012 | DOI | MR | Zbl

[23] Ngaiming Mok Metric rigidity theorems on Hermitian locally symmetric manifolds, Series in Pure Mathematics, 6, World Scientific, 1989, xiv+278 pages | MR | Zbl

[24] David Mumford Hirzebruch’s proportionality theorem in the noncompact case, Invent. Math., Volume 42 (1977), pp. 239-272 | DOI | MR | Zbl

[25] Alan Michael Nadel The nonexistence of certain level structures on abelian varieties over complex function fields, Ann. Math., Volume 129 (1989) no. 1, pp. 161-178 | DOI | MR | Zbl

[26] Erwan Rousseau Hyperbolicity, automorphic forms and Siegel modular varieties, Ann. Sci. Éc. Norm. Supér., Volume 49 (2016) no. 1, pp. 249-255 | DOI | MR | Zbl

[27] Goro Shimura 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 | Zbl

[28] Jörg Winkelmann On Brody and entire curves, Bull. Soc. Math. Fr., Volume 135 (2007) no. 1, pp. 25-46 | DOI | Numdam | MR | Zbl

[29] Song-Yan Xie On the ampleness of the cotangent bundles of complete intersections, Invent. Math., Volume 212 (2018) no. 3, pp. 941-996 | MR | Zbl

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