The Volume of K-Semistable Fano Manifolds
数学专题报告
报告题目(Title)：The Volume of K-Semistable Fano Manifolds
报告人(Speaker)：缪铭昊（南京大学）
地点(Place)：后主楼1223
时间(Time)：2025年3月26日（周四）16:00-17:00
邀请人(Inviter)：张科伟
报告摘要
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 CP^n, 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.
