Constructions of Kahler-Einstein metrics with negative scalar curvature

TL;DR

This paper proves that a sequence of algebraic metrics on Kahler manifolds with negative first Chern class converges uniformly to the Kahler-Einstein metric, including cases with singularities.

Contribution

It establishes convergence of Tsuji's algebraic metrics to Kahler-Einstein metrics on manifolds with negative first Chern class, extending to singular cases.

Findings

Convergence of algebraic metrics to Kahler-Einstein metrics on manifolds with negative first Chern class

Extension of convergence results to algebraic surfaces of general type and orbifolds with singularities

Modified iterative construction achieves convergence in singular cases

Abstract

We show that on Kahler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by H. Tsuji converges uniformly to the Kahler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's iterative construction.