Holomorphic morse inequalities and the Green-Griffiths-Lang conjecture

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Abstract

The goal of this work is to study the existence and properties of non entire curves f: ℂ → X drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must satisfy certain global algebraic or differential equations as soon as X is projective of general type. By means of holomorphic Morse inequalities and a probabilistic analysis of the cohomology of jet spaces, we are able to prove a significant step of a generalized version of the Green-Griffths-Lang conjecture on the algebraic degeneracy of entire curves.

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Demailly, J. P. (2011). Holomorphic morse inequalities and the Green-Griffiths-Lang conjecture. Pure and Applied Mathematics Quarterly, 7(4), 1165–1207. https://doi.org/10.4310/PAMQ.2011.v7.n4.a6

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