Birational geometry of foliations

Speaker：

Paolo Cascini (Imperial College, London)

Time：

Tues. & Thur., 9:30-11:00 am, Mar. 3-Mar. 26, 2026

Venue：

B725, Shuangqing Complex Building A

Description:

We will continue the study of the birational geometry of foliations on complex varieties and in positive characteristic. Although there will be minimal overlap with the previous lectures, no specific background will be assumed beyond general knowledge of birational geometry.

We will begin with a review of the basic results in the birational geometry of foliated surfaces. We will then discuss the Miyaoka–Campana–Păun Theorem, which relates the geometry of a variety to the positivity properties of its foliations.

Subsequently, we will develop key tools, including the study of singularities of foliations. In the final part of the course, we will present some of the main results of the Minimal Model Program (MMP) for foliations in higher dimensions and discuss applications, including results related to the canonical bundle formula.