威尼斯人娱乐场

Speaker

Caucher Birkar

Time

Every Friday 13:30-15:05

from 2025-02-21

Venue

B725

Shuangqing Complex Building A

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.

Prerequisites

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

References

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.