Viehweg's hyperbolicity conjecture for families with maximal variation

TL;DR

This paper proves Viehweg's hyperbolicity conjecture for families with maximal variation using Hodge modules, showing their base spaces are of log general type, advancing understanding of the geometric properties of such families.

Contribution

The paper introduces a Hodge module approach to establish Viehweg's hyperbolicity conjecture for families with maximal variation and fibers of general type.

Findings

Base spaces of such families are of log general type.

Construction of Viehweg-Zuo sheaves using Hodge modules.

Supports hyperbolicity conjecture in this context.

Abstract

We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on the base spaces of families with maximal variation and fibers of general type, or more generally whose geometric generic fiber has a good minimal model. We deduce Viehweg's hyperbolicity conjecture in this context, namely the fact that the base spaces of such families are of log general type. This is approached as part of a general problem of identifying what spaces can support Hodge theoretic objects with certain positivity properties.