Title: Orbifold modification of complex analytic varieties

Abstract: The main objective of this lecture is to study reflexive sheaves on Kaehler varieties with klt singularities, which appear naturally in the theory of Minimal Model Program.Since klt singularities are quotient singularities in codimension 2, we will construct a modification, with quotient singularities only, which is an isomorphism in codimension 2. With such a modification, we can define orbifold Chern classes, and prove a Bogomolov inequality on them.