Entire curves in complex projective varieties and differential equations

[D-EG00] Demailly, J.-P., El Goul, J.: Hyperbolicity of Generic Surfaces of High Degree in Projective 3-Space.

Jean-Pierre Demailly (Grenoble I), 16/04/2009 Entire curves and algebraic differential equations / IF - IMPA..

The latter conjecture asserts that every entire curve drawn on a projective variety of general type should satisfy a global algebraic equation; via a probabilistic

The goal of these notes is to study complex varieties, mainly compact or projective algebraic ones, through a few geometric questions related to hyperbolicity in the sense of

Also, in 2007, Demailly pioneered the use of holomorphic Morse inequalities to construct jet differentials; in 2010, Diverio, Merker and Rousseau were able in that way to prove

We prove, using results of SMYTH [S], that if C is an irreducible curve of degree < 2n ifn <^ 7, and <^ 1.7719 n ifn > 7, on a simple principally polarized abelian variety

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We would like to thank our colleagues Franc Forstneri5 and Josip Globewflk for extremely helpful discussions about this proposition.. The present article is an