Hermite--Einstein metrics in singular settings

TL;DR

This paper proves the existence of Hermite--Einstein metrics for stable sheaves on singular Kähler spaces, providing new insights into geometric structures in singular settings, especially with klt singularities.

Contribution

It establishes the existence of Hermite--Einstein metrics in singular contexts, extending classical results to more general and singular varieties.

Findings

Existence of Hermite--Einstein metrics for stable reflexive sheaves on compact normal Kähler spaces.

More precise results when the background variety has klt singularities.

Advancement in understanding geometric structures in singular algebraic varieties.

Abstract

In this article we pursue the following main goals. In the first place, we establish the existence of "estimable" Hermite--Einstein metrics for stable reflexive coherent sheaves on compact normal K\"ahler spaces. If moreover the background variety has klt singularities, we obtain a much more precise result.