Hodge sheaves for singular families

Abstract: This is a report on joint work with Behrouz Taji. Given a flat projective morphism $f:X\to B$ 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.

algebraic geometry

Audience: researchers in the topic

Columbia algebraic geometry seminar