On the moduli of Kahler-Einstein Fano manifolds

TL;DR

This paper establishes that Kahler-Einstein Fano manifolds with finite automorphism groups form a well-behaved moduli space with quotient singularities, and explores their boundary limits as Q-Fano varieties.

Contribution

It proves the existence of a Hausdorff moduli space for Kahler-Einstein Fano manifolds with finite automorphisms and discusses the boundary compactification involving Q-Fano varieties.

Findings

Moduli space is Hausdorff with quotient singularities.

Finite automorphism groups characterize the moduli space.

Boundary points include Q-Fano varieties.

Abstract

We prove that Kahler-Einstein Fano manifolds with finite automorphism groups form Hausdorff moduli algebraic space with only quotient singularities. We also discuss the limits as Q-Fano varieties which should be put on the boundary of its canonical compactification.