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K-stability and Products of K-moduli spaces

来源: 10-10

时间:Fri., 15:30-16:30, Oct. 11, 2024

地点:B725, Shuangqing Complex Building

主讲人:Theodoros Papazachariou (YMSC)

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.

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