Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.3636
- Bibcode:
- 2010arXiv1011.3636D
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 38 pages, dedicated to the memory of Eckart Viehweg