Viehweg's hyperbolicity conjecture is true over compact bases

TL;DR

This paper proves Viehweg's hyperbolicity conjecture for compact bases and certain non-uniruled bases, confirming that the base space of maximal variation families of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.

Contribution

It establishes the conjecture over broader classes of bases, including compact and non-uniruled compactifications, advancing understanding of hyperbolicity in algebraic geometry.

Findings

Viehweg's hyperbolicity conjecture is confirmed for compact bases.

The base space of maximal variation families is shown to be of log-general type.

The result applies to bases with non-uniruled compactification.

Abstract

We prove Viehweg's hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the the base space of a maximal variation family of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.