On the volume of K-semistable Fano manifolds

：缪铭昊（南京大学）
：2025-12-10 10:30
：海韵园实验楼S205

报告人：缪铭昊（南京大学）

时  间：2025年12月10日10:30

地  点：海韵园实验楼S205

内容摘要:

In 2015, K. Fujita showed that for any n-dimensional K-semistable Fano manifold, the anti-canonical volume is always less than or equal to that of complex projective space (CP^n). In this talk, I will discuss my recent joint work with Chi Li on characterizing the second-largest volume. We prove that for any n-dimensional K-semistable Fano manifold X that is not isomorphic to CPⁿ, the volume is at most 2n^n, with the equality holds if and only if X is a smooth quadric hypersurface or CP^1 × CP^{n-1}. This result applies, in particular, to all Fano manifolds admitting Kähler-Einstein metrics. Our proof is based on a new connection between K-stability and minimal rational curves.

个人简介：

缪铭昊，南京大学数学学院在读博士研究生。缪铭昊的研究领域是K稳定性与Fano流形相关的几何问题。其研究工作发表在Math. Ann.等知名期刊。

 

联系人：周楚宇