Lectures on Algebraic Geometry

任课教师 Speaker:考切尔·比尔卡尔 (Caucher Birkar)
时间 Time: 每周五 北京时间17:00 -19:00,2020-9-4/11/18/25 & 10-9
地点 Venue:Zoom Meeting ID:849 963 1368 Tencent Meeting ID:585 2904 5552

课程描述 Description

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.

预备知识 Prerequisites

Topics aimed to be covered:


Lecture 1, Singularities: definition and examples of singularities, some basic properties.
Video: http://ymsc.tsinghua.edu.cn/cn/content/show/99-28.html

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

Lecture 2, Birational geometry of surfaces: contractions, minimal model program, classification.
Video: http://ymsc.tsinghua.edu.cn/cn/content/show/99-30.html

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

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

Video:http://ymsc.tsinghua.edu.cn/cn/content/show/99-36.html

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.
Videohttp://ymsc.tsinghua.edu.cn/cn/content/show/99-50.html

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

参考资料 References

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