Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality

Details Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality

2008-08-18

arxiv.org/abs/0808.2444v2

Mathematics

Algebraic Geometry

12 pages; some improvements according to suggestions from the referees, to appear in Duke Math. J

Scientific paper

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.

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