Constant Scalar Curvature K\"ahler Metrics on Resolutions of an Orbifold Singularity of Depth 1

TL;DR

This paper constructs new constant scalar curvature Kähler metrics on resolutions of specific orbifold singularities, expanding the class of known examples in complex differential geometry.

Contribution

It introduces a method to produce CSC Kähler metrics on resolutions of orbifolds with type I singularities along higher codimension suborbifolds.

Findings

New examples of CSC Kähler metrics on orbifold resolutions

Extension of existing methods to higher codimension singularities

Potential applications to complex geometric classification

Abstract

We construct new examples of constant scalar curvature K\"{a}hler metrics on suitable resolutions of certain constant scalar curvature K\"{a}hler orbifolds with type I singularities, in the sense of Apostolov--Rollin, along a suborbifold of complex codimension greater than 2.