## Algebraic geometry

### Prof. Ugo Bruzzo

Number of cycles: 2

First semester: Thu 16:30-18, Fri 14:30-16 (starting from October 20)

Content:

- Schemes.
- Sheaves.
- Schemes.
- Morphisms of schemes.
- Divisors.
- Projective morphisms.
- Differentials.
- Cohomology.
- Derived functors.
- Sheaf cohomology, Ext groups and sheaves.
- Cech cohomology.
- Higher direct images.
- Flat and smooth morphisms.
- The semicontinuity theorem.
- Curves.
- Riemann-Roch theorem.
- Hurwitz theorem.
- Projective curves.