Stability conditions on irreducible singular curves of genus one.
by
Bernd Kreussler
MIC Limerick, Ireland
Coauthors: Igor Burban

Motivated by the study of Dirichlet branes in string theory, T. Bridgeland introduced the notion of a stability condition on a triangulated category. The main ingredient for this notion is a generalisation of Harder-Narasimhan filtrations for objects in a triangulated category.

We use this concept in order to gain a good understanding of the structure of the bounded derived category of coherent sheaves on a singular cubic curve. As a result we give a description of the group of exact auto-equivalences of this category, we describe all t-structures and the moduli space of stability conditions on it. Moreover, we describe all spherical objects in this category.

Our methods allow us to understand indecomposable objects in this category, which may be interesting from a representation theory perspective.

Date received: March 15, 2005