Birational geometry of foliations

Speaker：

Paolo Cascini

Imperial College, London

Time：

Wed.& Fri., 9:50-11:25 am

July 2-July 11, Aug. 27-Sept. 26, 2025

Venue：

B725, Shuangqing Complex Building A

Description：

In this course, we will explore the birational geometry of foliations on complex varieties and in positive characteristic. We will begin with the theory of foliations on complex algebraic surfaces, introducing key concepts and examples. Afterward, we will discuss the Miyaoka-Campana-Păun Theorem, which connects the geometry of a variety with the positivity properties of its foliations. We will develop tools such as the study of singularities of foliations and Reeb's stability theorem. In the final part of the course, we will cover some of the main results of the Minimal Model Program (MMP) for foliations in higher dimension and discuss applications, including results related to the canonical bundle formula.