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.

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.

Topics aimed to be covered:

Lecture 1, Singularities: definition and examples of singularities, some basic properties.
Video:

Note：/uploads/file/2020/20201019/20201019092437_50163.pdf

Lecture 2, Birational geometry of surfaces: contractions, minimal model program, classification.

Note：/uploads/file/2020/20201019/20201019092500_67690.pdf

Lecture 3, Quotient varieties: definition and examples of local and global quotients, singularities.

Note：/uploads/file/2020/20201019/20201019092514_32004.pdf


Lecture 4, The weighted projective space: definition as quotient of projective space, singularities, Fano property, unboundedness, anti-canonical volume.
Video：

Note：/uploads/file/2020/20201019/20201019092530_53480.pdf

Lecture 5, Cremona groups: definition, examples, Jordan property for dimension two with proof, simple finite subgroups.

Video： http://ymsc.tsinghua.edu.cn/cn/content/show/99-52.html

Note：/uploads/file/2020/20201019/20201019092553_17958.pdf

Contact person: Prof. Si Li
Email: sili@mail.tsinghua.edu.cn

Zoom Meeting ID：849 963 1368   

Passcode: YMSC

Tencent Meeting ID：585 2904 5552

Passcode: 2020