Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension

Abstract

Given a smooth complex projective variety X, a line bundle L of X an element v of H^1(O_X) and a section s in H^0(L) that deforms to first order in the direction v, we give a sufficient condition on v in terms of Koszul cohomology for this first order deformation to extend to an analytic deformation. We apply this result to improve known results on the paracanonical system of a variety of maximal Albanese dimension, due to Beauville in the case of surfaces and to Lazarsfeld-Popa in higher dimension. In particular, we prove the inequality p_g(X)>=χ(K_X)+q(X)-1 for a variety X of maximal Albanese dimension without irregular fibrations of Albanese general type.

References in corpus (1)

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

Cited by in corpus (6)

• Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties
• Relative Clifford inequality for varieties fibered by curves
• A note on surfaces with $p_g=q=2$ and an irrational fibration
• Severi inequality for varieties of maximal Albanese dimension
• Some results on deformations of sections of vector bundles
• A twisted bicanonical system with base points