Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture

Details Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture

2010-11-16

arxiv.org/abs/1011.3636v2

Mathematics

Algebraic Geometry

38 pages, dedicated to the memory of Eckart Viehweg

Scientific paper

The goal of this work is to study the existence and properties of non constant entire curves f 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 reach a significant step towards a generalized version of the Green-Griffiths-Lang conjecture.

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