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arXiv · 2012.02018

Continuity of singular K\"ahler-Einstein potentials

Vincent Guedj·Henri Guenancia·Ahmed Zeriahi
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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.

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Vincent Guedj, Henri Guenancia, Ahmed Zeriahi. 2020-12-03. Continuity of singular K\"ahler-Einstein potentials. https://arxiv.org/abs/2012.02018

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