The moduli space of Fano manifolds with Kähler–Ricci solitons

Abstract

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with Kähler–Ricci solitons. This enlarges the moduli space of Fano manifolds with Kähler–Einstein metrics. We discover a moment map picture for Kähler–Ricci solitons, and give complex analytic charts on the topological space consisting of Kähler–Ricci solitons, by studying differential geometric aspects of this moment map. Some stacky words and arguments on Gromov–Hausdorff convergence help to glue them together in the holomorphic manner.