Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality
Algebraic Geometry
2019-12-19 v2
Abstract
We extend to manifolds of arbitrary dimension the Castelnuovo-de Franchis inequality for surfaces. The proof is based on the theory of Generic Vanishing and higher regularity, and on the Evans-Griffith Syzygy Theorem in commutative algebra. Along the way we give a positive answer, in the setting of K\"ahler manifolds, to a question of Green-Lazarsfeld on the vanishing of higher direct images of Poincar\'e bundles. We indicate generalizations to arbitrary Fourier-Mukai transforms.
Keywords
Cite
@article{arxiv.0808.2444,
title = {Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality},
author = {Giuseppe Pareschi and Mihnea Popa},
journal= {arXiv preprint arXiv:0808.2444},
year = {2019}
}
Comments
12 pages; some improvements according to suggestions from the referees, to appear in Duke Math. J