A generalization of the Castelnuovo-de Franchis inequality

الأصل · EN

We give a lower bound on the Hodge number h²,⁰(X), where X is an irregular compact Kähler (or smooth complex projective) variety, in terms of the minimal rank of an element in the kernel of the wedge product map ψ₂: Λ² H⁰(X,Ωₓ¹) -> H⁰(X,Ωₓ²). As a consequence, we obtain a generalization to higher dimensions of the Castelnuovo-de Franchis inequality for surfaces, improving some results of Lazarsfeld and Popa and Lombardi for threefolds and fourfolds.