# 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.

## Key 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.