Viehweg hyperbolicity for Whitney equisingular families with Gorenstein rational singularities

TL;DR

This paper proves a hyperbolicity property for certain families of algebraic varieties with specific singularities, extending Viehweg's conjecture using advanced Hodge module techniques.

Contribution

It establishes Viehweg's hyperbolicity conjecture for Whitney equisingular families with Gorenstein rational singularities, introducing intersection complexes as Hodge modules in the proof.

Findings

Base spaces of such families are of log general type.

The construction suggests an equisingular stratification of the moduli space.

First step towards hyperbolic stratification of moduli spaces.

Abstract

We prove the analogue of Viehweg's hyperbolicity conjecture for Whitney equisingular families of projective varieties with Gorenstein rational singularities whose geometric generic fiber has a good minimal model. Namely, for such families with maximal variation, the base spaces are of log general type. The main new ingredient is the use of intersection complexes as Hodge modules in the construction of logarithmic Higgs sheaves by Viehweg-Zuo and Popa-Schnell. This construction suggests an equisingular stratification of the moduli space of varieties of general type, with each stratum being hyperbolic, and our result is a first step in this direction.