Bogomolov-Gieseker inequality for log terminal K\"ahler threefolds

TL;DR

This paper extends the Bogomolov-Gieseker inequality to stable sheaves on three-dimensional compact K"ahler spaces with log terminal singularities, advancing the understanding of stability conditions in complex geometry.

Contribution

It establishes an orbifold version of the Bogomolov-Gieseker inequality for stable -sheaves on log terminal K"ahler threefolds, a novel generalization in complex geometry.

Findings

Proves the orbifold Bogomolov-Gieseker inequality for stable -sheaves

Extends stability results to threefolds with singularities

Provides tools for further research in K"ahler geometry

Abstract

In this article we are mainly concerned with three dimensional compact K\"ahler spaces with log terminal singularities. We establish the orbifold version of the Bogomolov-Gieseker inequality for stable $\mathbb Q$-sheaves.