K-stability and Products of K-moduli spaces

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Theodoros Papazachariou (YMSC)

Time：

Fri., 15:30-16:30, Oct. 11, 2024

Venue：

B725, Shuangqing Complex Building

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title：

K-stability and Products of K-moduli spaces

Abstract：

In recent years, K-stability has made extraordinary progress in constructing moduli spaces of Fano varieties and log Fano pairs. This construction, however, is not explicit, and needs to be studied on a case-by-case basis to explicitly describe specific examples of moduli spaces for Fano varieties. In this talk I will give a brief introduction to K-stability, and describe the local and global structures and properties of the K-moduli space of products of Fano varieties. I will then provide a method to study K-moduli spaces of products of Fano varieties. I will demonstrate that a connected component of the K-moduli stack that contains a product, must only contain product Fano varieties. I will also demonstrate that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product and show that it is an isomorphism under specific conditions. Using this I will present some explicit examples of reduced connected components of the K-moduli stack of Fano threefolds, and log Fano pairs.