This course is aimed to give students an introduction to the theory of algebraic curves and surfaces. In particular, it aims to develop the students' geometric intuition and combined with the basic algebraic geometry courses to build a strong foundation for further study.
Contents
- Riemann surfaces,
nonsingular algebraic curves
- Divisors and line bundles, linear
systems
- Riemann-Roch, Riemann-Hurwitz, etc.
- Plane curve
singularities, blowing up
- Algebraic surfaces, intersection forms
- Riemann-Roch for surfaces
- Kodaira dimension
- Ruled surfaces,
rational surfaces
- Elliptic surfaces, K3, Enriques surfaces, etc.
- Birational classification (or MMP) for surfaces
- Further topics
- Professor: Oscar Salomon Kivinen
- Teacher: Francesca Carocci
