On the period map for abelian covers of projective varieties

Abstract

This paper is devoted to the study of the period map for abelian covers of smooth projective varieties of dimension n ≥ 2. Our viewpoint is very close to that of Green in [8], namely we look for results that hold for abelian covers of an arbitrary variety whenever certain ampleness assumptions on the building data defining the cover are satisfied. We focus on two questions: the infinitesimal and the variational Torelli problems. Infinitesimal Torelli for the periods of k-forms holds for a smooth projective variety X if the map H(X,TX) → ⊕pHom (

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