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.

Video: https://space.bilibili.com/1309483916/channel/seriesdetail?sid=2109164&ctype=0

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

Note：[PDF]

Lecture 2, Birational geometry of surfaces: contractions, minimal model program, classification.
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Lecture 3, Quotient varieties: definition and examples of local and global quotients, singularities.

Note：[PDF]

Lecture 4, The weighted projective space: definition as quotient of projective space, singularities, Fano property, unboundedness, anti-canonical volume.
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Lecture 5, Cremona groups: definition, examples, Jordan property for dimension two with proof, simple finite subgroups.

Note：[PDF]

                  

Contact person: Prof. Si Li

Email: sili@mail.tsinghua.edu.cn