On the moduli space of ricci flat metrics on a K3 surface

TL;DR

This paper investigates the topological and cohomological properties of the moduli space of Ricci flat metrics on K3 surfaces, revealing its simple connectivity and cohomology structure.

Contribution

It proves the simple connectivity of the moduli space and determines its rational cohomology to match that of a specific automorphism group.

Findings

The moduli space of Ricci flat metrics on K3 surfaces is simply connected.

Its rational cohomology matches that of the automorphism group of the K3 lattice.

Includes orbifold metrics in the analysis.

Abstract

We show that the moduli space of Ricci flat metrics of unit volume (including orbifold metrics) on a K3 surface is simply connected and that it has the same rational cohomology as the automorphism group of the K3 lattice $(-E_8)^{\oplus 2}\oplus U^{\oplus 3}$.