Removable singularities of the CscK metric

TL;DR

This paper proves that certain conically singular constant scalar curvature Kähler (CscK) metrics, which are bounded near divisors, can be smoothly extended across the divisor, ensuring regularity.

Contribution

It establishes conditions under which a CscK metric with controlled singularities extends smoothly across divisors, advancing understanding of metric regularity in complex geometry.

Findings

CscK metrics with specific bounds are smooth across divisors

The paper provides conditions for removability of singularities

Extends regularity results for singular Kähler metrics

Abstract

In this paper, we consider a CscK metric defined away from divisor and with metric upper bound and lower bound going to zero in certain rate. And we'll prove that this "nicely" behaved metric is a smooth CscK metric across the divisor.