On the resolution of constant scalar curvature K\"ahler orbifolds

TL;DR

This paper establishes conditions under which compact Kähler orbifolds with constant scalar curvature and singularities can be desingularized into smooth Kähler manifolds, extending previous results to orbifolds with nontrivial holomorphic vector fields.

Contribution

It generalizes prior desingularization results to orbifolds with singularities and nontrivial holomorphic vector fields, providing explicit conditions and examples.

Findings

Derived sufficient conditions for desingularization

Extended desingularization techniques to orbifolds with singularities

Presented explicit examples illustrating the theory

Abstract

In this paper, given a compact Kcsc orbifolds of any dimension and with nontrivial holomorphic vector fields, we find sufficient conditions on the position of singular points in order to admit a Kcsc desingularization, generalizing the result of the first author with F. Pacard in the case of blowing up smooth points. A series of explicit examples are discussed.