Instructor: Caucher Birkar，2018 Fields Medallist

Email: birkar@mail.tsinghua.edu.cn

Time: Thursday 13:30-15:05, 2022 Spring

Course Description:

This year-long course is an introduction to birational geometry, a central area of algebraic geometry. The aim is to introduce some of the core concepts and techniques in the birational classification theory of algebraic varieties. It will be suitable for advanced undergraduate students, PhD students, postdocs, and others interested in the subject. historical background. The audience is assumed to be familiar with basics of algebraic geometry.

Prerequisites:

The audience is assumed to be familiar with basics of algebraic geometry.

Course Outline:

1. Curves

2. Surfaces

3. Explicit geometry

4. Bend and break technique

5. Singularities and pairs

6. Kodaira dimension

7. MMP in higher dimension, minimal models and Mori fibre spaces, flips and finite generation

8. Generalised pairs

9. Boundedness and moduli of varieties

10. Sarkisov program, etc.