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arXiv · 2512.22273

Orbifold Chern classes and Bogomolov-Gieseker inequalities

Wenhao Ou
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Abstract

Assume that $X$ is a compact complex analytic variety which has quotient singularities in codimension 2, and that $\mathcal{F}$ is a reflexive sheaf on $X$. Using orbifold modifications, we can define first and second homological Chern classes for $\mathcal{F}$. If in addition $X$ has a K\"ahler form $\omega$ and $\mathcal{F}$ is $\omega$-stable, then we deduce Bogomolov-Gieseker inequality on the orbifold Chern classes of $\mathcal{F}$.

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Wenhao Ou. 2025-12-25. Orbifold Chern classes and Bogomolov-Gieseker inequalities. https://arxiv.org/abs/2512.22273

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