Abstract:
The space of Bridgeland stability conditions on a given triangulated category is a complex manifold, which gives us a way to extract geometry from homological algebra. An explicit description is only known in a few cases. In this talk, I will discuss two approaches to studying stability conditions on derived categories of surfaces that are free quotients by finite abelian groups. One method is via Le Potier functions, which characterise the existence of slope-semistable sheaves. The second method uses Deligne’s notion of group actions on triangulated categories to describe a connected component of so-called geometric stability conditions inside the stability manifold of these free abelian quotients when the cover has finite Albanese morphism. A consequence of this is a disproof of the expectation that surfaces with irregularity 0 always admit a wall of the geometric chamber. This is based on arXiv:2307.00815.
- Organizer: Center for Kvantematematik
- Address: Campusvej 55, 5230 Odense M
- Contact Email: qm@sdu.dk
- Add to your calendar: https://eom.sdu.dk:443/events/ical/a2e9c98b-1e73-4573-ba3e-47590355147c