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

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.