Smoothing conic K\"ahler metrics with uniformly upper bisectional curvature bound

TL;DR

This paper develops a method to smooth conic K"ahler metrics with a uniform upper bisectional curvature bound, aiding the study of conical K"ahler-Einstein metrics and Ricci flow.

Contribution

It introduces a smoothing sequence for conic K"ahler metrics under an upper bisectional curvature bound, including new background metrics for complex divisor configurations.

Findings

Constructed smoothing sequence for conic metrics

Extended methods to metrics with higher multiplicity points

Facilitates analysis of conical K"ahler-Einstein metrics

Abstract

Based on C. Li and Y. Rubinstein's upper bisectional curvature bound estimate for the conic K\"ahler metric, we can construct a smoothing sequence for the conic metric with uniformly upper bisectional curvature bound. For the conic metric along a simple normal crossing divisor with triple or higher multiple points we may need to choose a new background K\"ahler metric in the same cohomology class of the original background metric. This setting will be helpful to the study of conical K\"ahler-Einstein metrics and conical K\"ahler-Ricci flow.