Continuity of singular K\"ahler-Einstein potentials
Complex Variables
2021-09-22 v2 Differential Geometry
Abstract
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Amp\`ere equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity result. A consequence of our results is that K\"ahler-Einstein potentials are continuous at isolated singularities. Next, we establish the global continuity of solutions to DCMAE when the reference class belongs to the real N\'eron-Severi group. This yields in particular the continuity of K\"ahler-Einstein potentials on any irreducible Calabi-Yau variety.
Cite
@article{arxiv.2012.02018,
title = {Continuity of singular K\"ahler-Einstein potentials},
author = {Vincent Guedj and Henri Guenancia and Ahmed Zeriahi},
journal= {arXiv preprint arXiv:2012.02018},
year = {2021}
}
Comments
19 pages, v2: final version, to appear in IMRN. Expanded Sections 1&2 to detail the stability estimate and removed Section 4