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).

Here is the detailed schedule.
Office hours: Just drop me an email.

Material

Lecture notes.
Exercise sheets: 1, 2, 3, 4, Warm-up.

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

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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