Orbifold modifications of complex analytic varieties

Abstract

We prove that if $X$ is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism $f:Y\to X$, such that $Y$ has quotient singularities, and that the indeterminacy locus of $f^{-1}$ has codimension at least 3 in $X$. As an application, we deduce the Bogomolov-Gieseker inequality on orbifold Chern classes for stable reflexive coherent sheaves on compact Kähler varieties which have quotient singularities in codimension 2.

The major part of the paper is replaced by the paper "Orbifold modifications of complex analytic spaces" by János Kollár and Wenhao Ou. The part on Bogomolov-Gieseker inequalities is splitted into a short note