Kahler-Ricci shrinkers and Fano fibrations

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: https://ymsc.tsinghua.edu.cn/info/1053/1730.htm