GAAG seminar - Holomorphic symplectic manifolds from semistable Higgs bundles
Event details
| Date | 06.03.2025 |
| Hour | 13:15 › 15:00 |
| Speaker | Riccardo Carini |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Moduli spaces of semistable Higgs bundles are natural examples of non-compact holomorphic symplectic varieties. When the rank and degree are not coprime, they develop singularities and almost never admit symplectic resolutions. The only known exception—rank 2 and genus 2—can be viewed as a deformation of O’Grady’s exceptional examples in the setting of sheaves on K3 surfaces.
I will show that a similar phenomenon occurs in the genus 3 hyperelliptic case, once we pass to the quotient by the hyperelliptic involution, yielding examples of holomorphic symplectic manifolds arising from singular moduli spaces.
If time permits, I will discuss the compact analogue given by Beauville—Mukai systems and the additional difficulties that emerge in this setting.
Practical information
- Informed public
- Free
Contact
- Laetitia Al-Sulaymaniyin