Sandor Kovacs, Hodge Sheaves for Singular Families

This is a report on joint work with Behrouz Taji. Given a flat projective morphism f : X → B of complex varieties, assuming that B is smooth, we construct a functorial system of reflexive Hodge sheaves on B . If in addition, X is also smooth then this system gives an extension of the Hodge bundle underlying the VHS of the smooth locus of f . This in turn provides a criterion that all VHSs of geometric origin must satisfy. As an independent application we prove a singular version of Viehweg’s conjecture about base spaces of families of maximal variation.