Continuity of Monge-Amp{\`e}re Potentials in Big Cohomology Classes

TL;DR

This paper extends existing methods to prove that solutions to degenerate complex Monge-Ampère equations are continuous on a Zariski open set, with applications to singular Kähler-Einstein metrics on certain varieties.

Contribution

It generalizes DiNezza-Lu's approach to big cohomology classes, establishing continuity of solutions in a broader setting and applying this to singular Kähler-Einstein metrics.

Findings

Solutions are continuous on a Zariski open set

Singular Kähler-Einstein potentials are continuous on the ample locus

Extension of continuity results to big cohomology classes

Abstract

Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge-Amp{\`e}re equations on compact K{\"a}hler manifolds are continuous on a Zariski open set. This allows us to show that singular K{\"a}hler-Einstein metrics on log canonical varieties of general type have continuous potentials on the ample locus outside of the non-klt part.