Cubic threefolds with an involution and their intermediate Jacobians

Abstract

We study the moduli space of cubic threefolds admitting an involution via the period map sending such a cubic threefold to the invariant/anti-invariant part of the intermediate Jacobian. Our main result is global Torelli holds for the period map. Key ingredients of the proof include a description of the invariant/anti-invariant part of the intermediate Jacobian as a Prym variety and a detailed study of certain positive dimensional fibers of the corresponding Prym map. The proof also relies on the results of Donagi-Smith, Ikeda and Naranjo-Ortega on related Prym maps. This is joint work with S. Casalaina-Martin and L. Marquand.

Speaker

My research interest is algebraic geometry. In particular, I am interested in Hodge theory and its geometric applications, special varieties (e.g. K3 surfaces, cubic hypersurfaces, hyper-Kähler varieties), and geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains.