## Moduli spaces of algebraic curves

### Prof. Alessandro Verra

Number of cycles: 1

Second semester

Contents:

The course aims to introduce the basic tools for constructing the moduli space of curves M_g and then to present some properties of its birational geometry. There will be some emphasis on concrete examples, coming from the low genus cases and from classical algebraic geometry.

Tentative topics to be considered:

- deformation theory of curves;
- stable reduction theorem;
- Hilbert schemes of curves;
- construction of M_g via Kuranishi spaces;
- birational geometry of M_g in low genus.