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arXiv · 1802.08128

The moduli space of Fano manifolds with K\"ahler-Ricci solitons

Eiji Inoue
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Abstract

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with K\"ahler-Ricci solitons. This naturally enlarges the moduli space of Fano manifolds with K\"ahler-Einstein metrics, which was constructed by Odaka and Li-Wang-Xu. We discover a moment map picture for K\"ahler-Ricci solitons, and give complex analytic charts on the topological space consisting of K\"ahler-Ricci solitons, by studying differential geometric aspects of this infinite dimensional moment map. Some stacky words and arguments on Gromov-Hausdorff convergence help to glue them together in the holomorphic manner.

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Eiji Inoue. 2018-02-22. The moduli space of Fano manifolds with K\"ahler-Ricci solitons. https://arxiv.org/abs/1802.08128

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