Boundedness of singularities and discreteness of local volumes

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Ziquan Zhuang (Johns Hopkins University)

Time：

Fri., 09:00-10:00 am, Oct. 17, 2025

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

Boundedness of singularities and discreteness of local volumes

Abstract:

The local volume of a Kawamata log terminal (klt) singularity is an invariant that plays a central role in the local theory of K-stability. By the stable degeneration theorem, every klt singularity has a volume preserving degeneration to a K-semistable Fano cone singularity. I will talk about a joint work with Chenyang Xu on the boundedness of Fano cone singularities when the volume is bounded away from zero. This implies that local volumes only accumulate around zero in any given dimension.