This course is an introduction to intersection theory on algebraic varieties. An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foundation for further study.
Content
- Recap: Divisors, sheaf cohomology and morphisms to Grassmannians, canonical bundles
- Picard group of a variety. Jacobian variety of a curve
- Riemann-Roch theorem and Serre duality for curves
- Intersection theory on smooth surfaces, numerical equivalence
- Chow groups and Chow ring
- Chern classes and Segre classes
- Chow rings of Grassmannians
- Bezout theorem
- Introduction to classical Schubert calculus
- Hirzebruch-Riemann-Roch theorem and implications
- Professor: Eric Yen-Yo Chen
- Professor: Niccolò Giacomini
- Professor: Kamil Rychlewicz
