A generalization of the Castelnuovo-de Franchis inequality

Abstract

In this article we give a lower bound on h2,0 (X), where X is an irregular compact Kahler (or smooth complex projective) variety, in terms of the minimal rank of an element in the kernel of As a consequence, we obtain a generalization to higher dimensions of the Castelnuovode Franchis inequality for surfaces, improving some results of Lazarsfeld and Popa and Lombardi for threefolds and fourfolds.