On K\"ahler-Einstein surfaces with edge singularities

TL;DR

This paper characterizes certain logarithmic surfaces that can support Kähler-Einstein metrics with negative scalar curvature, specifically focusing on cases with small edge singularities along a normal crossing divisor.

Contribution

It provides a classification of logarithmic surfaces admitting Kähler-Einstein metrics with negative scalar curvature and edge singularities.

Findings

Characterization of logarithmic surfaces with Kähler-Einstein metrics

Conditions for existence of metrics with small edge singularities

Insights into the geometry of surfaces with singular metrics

Abstract

In this paper we characterize logarithmic surfaces which admit K\"ahler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.