Thom polynomials and the Green-Griffiths conjecture

Details Thom polynomials and the Green-Griffiths conjecture Thom polynomials and the Green-Griffiths conjecture

2010-11-21

arxiv.org/abs/1011.4710v1

Mathematics

Algebraic Geometry

61 pages

Scientific paper

In the first part of this paper we apply equivariant localization techniques to prove the Green-Griffiths conjecture for a generic projective hypersurface of dimension n and degree >2^{8nlogn}. In the second part we use a new geometric description of the invariant jet differentials on the hypersurface, and find a direct connection between Thom polynomials of Morin singularities and the Green-Griffiths problem. We prove, using equivariant localization, that a conjecture on the coefficients of the Thom polynomials implies the Green-Griffiths conjecture for generic projective hypersurfaces of dimension n and degree >n^6.

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