Kahler metrics with cone singularities along a divisor

TL;DR

This paper develops foundational methods for studying Kahler-Einstein metrics with cone singularities along divisors, focusing on how these metrics deform when the cone angle changes.

Contribution

It introduces new foundational techniques for analyzing the deformation of cone angles in Kahler-Einstein metrics with singularities.

Findings

Established a framework for cone angle deformation

Provided initial results on metric regularity near singularities

Laid groundwork for future studies on singular Kahler-Einstein metrics

Abstract

We develop some foundations for the study of Kahler-Einstein metrics with cone singularities transverse to a divisor. The main goal is a treatment of the deformation of the cone angle.