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.

考切尔·比尔卡尔现为英国剑桥大学教授。2018年8月获得了数学界最高奖菲尔兹奖。他的主要研究领域是代数几何(高维双有理几何，极小模型理论)，因在对不同类型的多项式方程进行的分类所作出的杰出贡献而获得2018年的菲尔茨奖。他证明了这类方程的无限多样性可以被分割成有限数量的类别，这在代数几何领域中是重大的突破。他对Fano簇的有限性的证明是他最有影响力的数学成果之一。

Topics aimed to be covered:

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

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.

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

联系人: 李思
Email: sili@mail.tsinghua.edu.cn

Zoom Meeting ID：849 963 1368   
密码: YMSC

腾讯会议 ID：585 2904 5552
密码: 2020