Kähler-Einstein Metrics for the Case of Negative and Zero Anticanonical Class

Abstract

Suppose M is a compact Kahler manifold of complex dimension m. We would like to prove in this chapter the existence of a Kahler-Einstein metric on M when the anticanonical class of M is either negative or zero. A Kahler-Einstein metric means a Kahler metric whose Ricci curvature is a constant multiple of the Kahler metric. First we formulate the problem in the form a Monge-Ampere equation.