Orbifold modifications of complex analytic varieties · arXivDesk
2401.07273Jan 14, 2024The 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
Orbifold modifications of complex analytic varieties
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→X, such that Y has quotient singularities, and that the indeterminacy locus of f−1
Nearby in the stack
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.