Mathematical Research Letters

Volume 28 (2021)

Number 5

Some criteria for uniform $K$-stability

Pages: 1613 – 1632



Chuyu Zhou (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Ziquan Zhuang (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


We prove some criteria for uniform K‑stability of $\operatorname{log}$ Fano pairs. In particular, we show that uniform K‑stability is equivalent to $\beta$-invariant having a positive lower bound. Then we study the relation between optimal destabilization conjecture and the conjectural equivalence between uniform K‑stability and K‑stability in twisted setting.

Received 9 December 2019

Accepted 25 March 2020

Published 16 August 2022