Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors

TL;DR

This paper establishes a priori estimates for constant scalar curvature Kähler metrics with conic singularities along normal crossing divisors, advancing understanding of their geometric properties and extending to twisted equations.

Contribution

It introduces new techniques to obtain higher order estimates for singular metrics and extends these estimates to twisted scalar curvature equations.

Findings

Zero order estimates via Alexandrov's maximum principle

Higher order estimates using Chen-Cheng's framework with new singularity handling techniques

Extension of estimates to twisted equations

Abstract

The purpose of this paper is to prove the a priori estimates for constant scalar curvature Kaehler metrics with conic singularities along normal crossing divisors. The zero order estimates are proved by a reformulated version of Alexandrov's maximum principle. The higher order estimates follow from Chen-Cheng's frame work, equipped with new techniques to handle the singularities. Finally, we extend these estimates to the twisted equations.