Orbifold modifications of complex analytic spaces

TL;DR

This paper demonstrates that any compact complex analytic space can be modified through orbifold techniques to become an orbifold, preserving local structures over certain loci.

Contribution

It introduces a method to obtain orbifold modifications of complex analytic spaces that are isomorphic over their locally trivial orbifold parts.

Findings

Existence of orbifold modifications for compact complex spaces

Preservation of local orbifold structures during modification

Application of orbifold techniques to complex analytic geometry

Abstract

We show that a compact, complex analytic space $X$ has a bimeromorphic orbifold modification that is an isomorphism over the locally trivial orbifold locus of $X$.