Moduli of Einstein Metrics on a K3 Surface and Degeneration of Type I

Abstract

This is an expository paper on the moduli space of K3 surfaces with Kähler–Einstein metric. We construct the universal family of Kähler–Einstein metrics on a K3 surface and show that it necessarily includes singular metrics such that some embedded 2-spheres have zero volume. We analyze this degeneration of Kähler–Einstein metrics in detail.