國立清華大學 數學系

Abstract：
The geometry of (mildly singular) Fano varieties is an exciting area of research in higher-dimensional birational geometry, featuring key developments such as Mori's bend-and-break technique, Birkar's proof of the Borisov-Alexeev-Borisov conjecture, and modern advancements in Donaldson-Tian's K-stability theory by Chenyang Xu and others. In this talk, we will focus on two other topics: Fano threefolds of maximal degree and Fano surfaces (del Pezzo surfaces) with unstable tangent bundles. We will show the existence of a singular K-polystable del Pezzo surface with an unstable tangent sheaf, a phenomenon not observed in smooth Fano manifolds. The main ingredient is the theory of algebraically integrable foliations. This work is a collaboration with Yen-An Chen at NCTS.