Structure & Description

This mini course is combined with 2023 HDAG workshop. We will have 4 invited lecturers to give mini-courses of 3 lectures each. The topics of the mini-courses focus on derived geometry and birational geometry. 

Talk Time (Agenda)

3/13 10:30-11:30

3/14 15:00-16:00

3/16 13:30-14:30

Abstract

The classical Minimal Model Program predicts that a complex projective manifold is either uniruled or it admits a minimal model, i.e. it is birational to a (possibly singular) projective variety whose canonical divisor is nef. The goal of these lectures is to explain an attempt to generalise this Program to the theory of foliations, focusing in particular on three dimensional varieties, on algebraically integrable foliations, and on some applications. 

Lecture I: An Introduction to the Minimal Model Program for foliations (video)

Abstract: We will survey some of the main tools in birational geometry, such as the bend and break, the cone theorem and the base point free theorem, both in the classical set-up and for foliations.

Lecture II: On foliations of co-rank one on a threefold. (video)

Abstract: I will give an overview of the Minimal Model Programs for co-rank one foliations on a normal complex threefold, with some applications on the study of singularities of such foliations.

Lecture III: Existence of flips. (video)

Abstract: We will discuss about existence of flips for foliations over a normal complex threefold and for algebraically integrable foliations.