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

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 Kähler manifolds, to a question of Green-Lazarsfeld on the vanishing of higher direct images of Poincaré bundles. We indicate generalizations to arbitrary Fourier-Mukai transforms.

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

References in corpus (1)

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications

Cited by in corpus (19)

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications
• Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension
• Derived invariants of irregular varieties and Hochschild homology
• Characterization of products of theta divisors
• Inequalities for the Hodge numbers of irregular compact Kaehler manifolds
• Cohomological rank functions and Syzygies of abelian varieties
• The cohomological support locus of pluricaonical sheaves and the Iitaka fibration
• Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds
• The geography of irregular surfaces
• Singularities of divisors of low degree on simple abelian varieties
• Generic Vanishing Fails for Surfaces in Positive Characteristic
• Irreducible Theta Divisors of PPAV's are Strongly F-regular
• Generic vanishing theory via mixed Hodge modules
• Syzygies, Pluricanonical Maps, and the Birational Geometry of Varieties of Maximal Albanese Dimension
• Hodge-Arakelov inequalities for family of surfaces fibered by curves
• On Severi type inequalities
• Some results on deformations of sections of vector bundles
• Grassmannian BGG Complexes and Hodge numbers of irregular varieties
• Irregular varieites with geometric genus one, theta divisors, and fake tori