SISSA Algebraic Geometry Seminar 2024–2025

This is the webpage of the SISSA Algebraic Geometry Seminar. The topics for the Spring Semester 2024–2025 will be Complex analytic methods, followed by Algebraic stacks. For the Complex analytic methods series, we meet on Tuesdays at 16:00 in Room 136.

Complex analytic methods – Detailed schedule

For the Complex analytic methods series, we meet on Tuesdays at 16:00 in Room 136.

• 21 January 2025, Žiga Gladek (SISSA): From smooth varieties to complex manifolds (Room 005)
• 28 January 2025, Michele Graffeo (SISSA): Algebraic curves and 1-dimensional manifolds (Room 005)
• 4 February 2025, Giordano Crimi (SISSA): Analytic coherent sheaves and GAGA
• 11 February 2025, Lorenzo Cortelli (SISSA): Applications of GAGA theorems

We mainly follow the English version of GAGA and FAC.

Algebraic stacks – Detailed schedule

For the stacks series, we meet on Mondays at 16:00 in Room 136.

• 24 Feb 2025, Solomiya Mizyuk (SISSA): Two exercises in descent theory
• 3 Mar 2025, Giordano Crimi (SISSA): Representable functors and issues with automorphisms
• 10 Mar 2025, Marco Miceli (SISSA): Sheaves on sites, topologies on Sch and comparisons
• 17 Mar 2025, Luca Morstabilini (SISSA): Groupoid fibrations and the 2–category of stacks; morphisms, substacks and 2–fibre products
• 24 Mar 2025, Nicolò Bignami (SISSA): Diagonal, inertia and automorphisms. Algebraic and Deligne–Mumfors stacks, algebraic spaces
• 31 Mar 2025, Lorenzo Cortelli (SISSA): Quotient stacks and examples
• 7 Apr 2025, Okke van Garderen (SISSA): Moduli of stable maps to projective space; universal curve, smoothness and components
• 14 Apr 2025, Emanuele Pavia (SISSA): Descent for quasicoherent sheaves
• 28 Apr 2025, Ian Selvaggi (SISSA): The stack of bundles and its smoothness over a curve

We mainly follow:

1. B. Fantechi, Stacks for everybody.
2. A. Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory.
3. A. Vistoli, Intersection theory on algebraic stacks and on their moduli spaces (§7).
4. D. Edidin, Notes on the Construction of the Moduli Space of Curves.
5. P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus.
6. M. Artin, Versal deformations and algebraic stacks.
7. D. Mumford, Picard groups of moduli problems.

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Past local seminars at SISSA

• Reading seminar on Complex analytic methods-Stacks (Spring 2025).
• Reading seminar on toric varieties (Fall 2024).
• Reading seminar on Hilbert schemes (Spring 2024).
• Reading seminar on deformation Theory (Fall 2023).
• Reading seminar on geometric invariant theory (Spring 2023).
• Reading seminar on Bridgeland stability conditions (Fall 2022).
• UNITS-SISSA Algebraic Geometry seminar (2020–2021).