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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