Algebraic Geometry (2024–2025)

This is the unofficial webpage of the course*Algebraic Geometry*, delivered in the academic year 2024–2025 to the Laurea Magistrale of the University of Trieste and the PhD program at SISSA. See also the 2024-25 academic calendar (including holidays).

For UNITS students: the winter exam session is

**7th January 2025 – 28th February 2025**.

Schedule and meetings

Lectures start on Tuesday, **1st October 2024** and follow the schedule:

- Tuesday 11:00–13:00 (Room 134) and 14:00–15:00 (Room 136)
- Wednesday 13:00–16:00 (Room 136).

__Office hours__: Just drop me an email.

Material

Lecture notes.

Exercise sheets:
1,
2,
3.

Bibliographic references

• Qing Liu, *Algebraic Geometry and Arithmetic Curves*, Oxford University Press (2006)

• Robin Hartshorne, *Algebraic Geometry*, GTM, volume 52, Springer New York (1977)

Possible exam topics

- Valuative criteria for separated and proper morphisms
- Infinitesimal lifting criterion for smoothness
- Cohomology and base change
- Cohomology of projective space
- Basic theory of abelian varieties
- Elliptic curves and their moduli
- Basic theory of stable sheaves
- The dualising complex
- The moduli space of stable bundles on a curve

Past Teaching

*Algebraic Geometry*(SISSA 2023–2024)*Algebraic Geometry*(SISSA 2022–2023)-
*Geometria e Algebra T*(Università di Bologna) -
*Localisation in Enumerative Geometry*, Spring 2021 PhD course - SISSA *Techniques in Enumerative Geometry*, Fall 2019 PhD course - SISSA*Algebraic Geometry MAT 630*, 2017 Master course - UiS (Norway)*Mathematical Methods 2 MAT200*(teaching assistant) - 2016, UiS (Norway)*Linear Algebra MAT110*(teaching assistant) - 2015, UiS (Norway)*Discrete Mathematics MAT120*- 2014, UiS (Norway)*Geometria e Algebra Lineare*(teaching assistant) - 2013, Politecnico di Torino