Continuity of Monge-Amp{\`e}re Potentials in Big Cohomology Classes
Differential Geometry
2021-09-16 v2 Analysis of PDEs
Complex Variables
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.
Keywords
Cite
@article{arxiv.2102.02704,
title = {Continuity of Monge-Amp{\`e}re Potentials in Big Cohomology Classes},
author = {Quang-Tuan Dang},
journal= {arXiv preprint arXiv:2102.02704},
year = {2021}
}
Comments
to appear in Int. Math. Res. Not