# YMSC-Lectures on Algebraic Geometry

**Speaker: Prof. Caucher Birkar**

Date & Time: Every Friday 5:00 – 7:00 pm. Beijing Time, 2020-9-4/11/18/25 & 10-9 ;

Zoom ID: 849 963 1368; Tencent ID: 585 2904 5552.

Date & Time: Every Friday 5:00 – 7:00 pm. Beijing Time, 2020-9-4/11/18/25 & 10-9 ;

Zoom ID: 849 963 1368; Tencent ID: 585 2904 5552.

**Abstract: **

The aim of these lectures is to introduce some topics in algebraic geometry to students who are familiar with basics of algebraic geometry roughly on the level of a first course on the subject. The students should make themselves familiar with divisors, the canonical divisor, the Riemann-Roch theorem for curves and surfaces, and should be willing to look up more basic results that we need as we progress.

The lectures are relatively elementary but they are related to current ongoing research in algebraic geometry.

**Topics aimed to be covered:**

**Lecture 1**

**S****ingularities: **definition and examples of singularities, some basic properties.

**Lecture 2**

**Birational geometry of surfaces:** contractions, minimal model program, classification.

**Lecture 3**

**Quotient varieties: **definition and examples of local and global quotients, singularities.

**Lecture 4**

**The weighted projective space: **definition as quotient of projective space, singularities, Fano property, unboundedness, anti-canonical volume.

**Lecture 5**

**Cremona groups: **definition, examples, Jordan property for dimension two with proof, simple finite subgroups.

**About Speaker**

Caucher Birkar is a professor at the University of Cambridge in the United Kingdom. His research area is algebraic geometry. In the International Congress of Mathematicians in 2018, Prof. Caucher Birkar was awarded the Fields medal, the highest honor for mathematicians, for his works on boundedness of Fano varieties and the minimal model program.