I will introduce the notion of a stability condition on a triangulated category through examples for which the space of all such, up to a natural notion of equivalence, is a modular curve. These will include the bounded derived category of coherent sheaves on an elliptic curve, a rational double point in two dimensions, and a three-dimensional example related to a moduli space of Higgs bundles. Time permitting I will discuss expected geometric structures on spaces of stability conditions which serve to clarify the relationship between the above three examples.
The modular curve as a space of stability conditions
11.10.2022 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: