Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties

Abstract

We give a sharp lower bound for the selfintersection of a nef line bundle $L$ on an irregular variety $X$ in terms of its continuous global sections and the Albanese dimension of $X$, which we call the Generalized Clifford-Severi inequality. We also extend the result to nef vector bundles and give a slope inequality for fibred irregular varieties. As a byproduct we obtain a lower bound for the volume of irregular varieties; when $X$ is of maximal Albanese dimension the bound is $Vol(X)\ge 2n!\chi {\omega }_X$ and it is sharp.

Final version, accepted for publication at Duke Math. J. Some typos corrected and new references added. Proof of Corollary B clarified. Exposition and proof of $5.2 simplified. Minor other changes in exposition

References in corpus (2)

• Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension
• An orbifold approach to Severi Inequality

Cited by in corpus (6)

• Linear systems on irregular varieties
• The eventual paracanonical map of a variety of maximal Albanese dimension
• Higher Dimensional Slope Inequalities for Irregular fibrations
• On Severi type inequalities
• Automorphisms of 3-folds of general type acting trivially on cohomology
• Some results on deformations of sections of vector bundles