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 $\mathcal{ F}$.
Categories: math.AG