Properness of the K-moduli space

Abstract: K-stability is an algebraic condition that characterizes the existence of Kahler-Einstein metrics on Fano varieties. Recently there has been a lot of work on the construction of the K-moduli space, i.e. a good moduli space parametrizing K-polystable Fano varieties. Motivated by results in differential geometry, it is conjectured that this K-moduli space is proper and projective. In this talk, I'll discuss some recent progress in birational geometry that leads to a full solution of this conjecture. Based on joint work with Yuchen Liu and Chenyang Xu.

algebraic geometry

Audience: researchers in the topic

( chat | slides | video )

Comments: The synchronous discussion for Ziquan Zhuang’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-12-17-zz (and will be deleted after ~3-7 days).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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