Overview
The study of the Moduli spaces of sheaves has important implications in different areas of mathematics, e.g. in enumerative geometry. In this reading seminar we will explore the existence as schemes of Moduli spaces of sheaves on K3 surfaces and their geometry. The seminar is mostly based on the book Geometry of Moduli spaces of sheaves by Huybrechts and Lehn. The prerrequisites for this seminar are the courses Algebraic Geometry I and II as taught in Bonn, or equivalently the second and third chapters of Hartshorne's book.
Schedule
The seminar will take place weekly during the Winter Semester 2024/25. We meet on fridays in the Mathematics Centre of the University of Bonn at SR0.008 from 18:00 to 20:00. Following talks have been programmed:
- Talk 1: Stability conditions (Katerina Papageorgiou Kafka)
- Talk 2: Representability of Quot scheme (Fabian Schnelle)
- Talk 3: Geometric invariant theory (Fabian Schnelle)
- Talk 4: Part I - Construction of the Moduli spaces of (semi)-stable sheaves (Jiaolong Zhang)
- Talk 5: Part II - Construction of the Moduli spaces of (semi)-stable sheaves (David Ĉadez)
- Talk 6: Deformation theory of sheaves (Esteban Castillo)
- Talk 7: K3 surfaces and sheaves on K3s (Philipp von Glasenapp)
- Talk 8: Smoothness and irreducibility of the Moduli spaces of stable sheaves (Alejandro Ovalle)
- Talk 9: Birational equivalence of moduli spaces and Hilbert schemes of points (Alejandro Ovalle)
- Talk 10: Moduli spaces and derived categories (Samir Geiger)
- Talk 11: Semi-stable vector bundles and p-adic Galois representations (Thomas Karamanis) - cancelled
Contact
If you have any questions or would like to participate, please contact me at alejandro.ovalle@uni-bonn.de.