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arXiv · 2401.07273

Orbifold modifications of complex analytic varieties

Wenhao Ou
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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 $f\colon Y\to X$, 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 K\"ahler varieties which have quotient singularities in codimension 2.

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Wenhao Ou. 2024-01-14. Orbifold modifications of complex analytic varieties. https://arxiv.org/abs/2401.07273

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