Research Group:

## Toric geometry

**Topics:**

- Toric varieties: fans, the orbit-cone correspondence, completeness, resolution of singularities.
- Divisors, line bundles and polytopes. Base-point free, nef and ample line bundles. Mori cone, class group, Picard group. Description in terms of polytopes.
- Cohomology of coherent sheaves on toric varieties. Reflexive sheaves, differential forms, toric Serre duality, cohomology of toric divisors.

**Note:** 20h from February 3 to March 4 + 12h from April 4 to 14 + 8h in June

## Algebraic Geometry

Tuesday 11:00-13:00 and Wednesday 14:00-16:00

**Content:**

Varietà algebriche proiettive e quasi proiettive. Fasci. Coomologia dei fasci. Spazi anellati e schemi. Fasci e divisori. Fibrati. Differenziali e divisore canonico. Geometria delle curve proiettive e teorema di Riemann-Roch.