Algebraic Geometry Seminar
Organizers：
Caucher Birkar，Jia Jia 贾甲
Speaker：
Song Sun 孙崧 (Zhejiang University)
Time：
Fri., 15:30-16:30, Mar. 28, 2025
Online：
Zoom Meeting ID: 262 865 5007
Passcode: YMSC
Venue：
B725, Shuangqing Complex Building A
Title:
Kahler-Ricci shrinkers and Fano fibrations
Abstract：
In this talk I will discuss complete (possibly non-compact) gradient shrinking Kahler-Ricci solitons, also known as Kahler-Ricci shrinkers, which are differential geometric objects arising from the study of singularities of Kahler-Ricci flows. We will first connect Kahler-Ricci shrinkers to algebraic geometry by showing that they are naturally quasi-projective varieties and admit the structure of a polarized Fano fibration (in the sense of minimal model program). The proof uses the boundedness result of Birkar for Fano type varieties. Then we will explain a Yau-Tian-Donaldson type conjecture for the existence of Kahler-Ricci shrinkers and a 2-step degeneration picture for determining a Kahler-Ricci shrinker at a finite time singularity of Kahler-Ricci flow. The latter is similar to the setting of metric tangent cones for singular Kahler-Einstein metrics. Based on joint work with Junsheng Zhang, arXiv:2410.09661.
Link: //ymsc.thsp18.com/info/1053/1730.htm
