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Complex Analysis and Geometry Seminar

Openness of uniformly valuative stability of polarized varieties and applications

Yaxiong Liu - Tsinghua University

Location:  Zoom
Date & time: Friday, 20 January 2023 at 9:30AM - 10:30AM

Title: Openness of uniformly valuative stability of polarized varieties and applications.

Abstract: In the study of K-stability, Fujita and Li proposed the valuative criterion of K-stability on Fano varieties, which has played an essential role of the algebraic theory of K-stability. Recently, Dervan-Legendre considered the valuative criterion of polarized varieties, which is a generalization of Fujita-Li criterion on Fano varieties. We will show that uniformly valuative stability is an open condition. We would like to study the valuative criterion for the Donaldson's J-equation. Motivated by the beta-invariant of Dervan-Legendre, we introduce a notion, the so-called valuative J-stability and prove that J-stability implies valuative J-stability. 

Zoom Link:

Meeting ID: 952 3723 4346
Password: 846718



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