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Title:
Uniqueness of K-polystable degenerations of Fano varieties
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Abstract:
In this talk, I will explain that given a family of Fano varieties over a punctured curve any K-polystable degeneration is unique. The result and its proof have a couple of interesting applications: (1) it is an input in constructing the separated good moduli space parametrizing K-polystable Fano varieties and (2) it can be used to show that K-polystable Fano varieties have reductive automorphism group. This talk is based on joint work with Jarod Alper, Daniel Halpern-Leistner, and Chenyang Xu.
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