Orbifold regularity of weak Kahler-Einstein metrics

TL;DR

This paper proves that limits of Kahler-Einstein manifolds are either smooth or orbifold outside a small subvariety, advancing understanding of their geometric structure in the non-collapsing case.

Contribution

It establishes orbifold regularity for Gromov-Hausdorff limits of Kahler-Einstein manifolds, showing they are smooth or orbifold outside a codimension at least 3 subvariety.

Findings

Limits are either smooth or orbifold outside a codimension 3 subvariety.

Provides a regularity result for non-collapsing Kahler-Einstein limits.

Advances understanding of geometric structure of Kahler-Einstein manifolds.

Abstract

In this note, we prove that any non-collapsing and compact Gromov-Hausdorff limit of Kahler-Einstein manifolds is either smooth or is orbifold outside a subvariety of complex codimension at least 3.