Stability conditions and the braid group

摘要

We find stability conditions [6, 3] on some derived categories of differential graded modules over a graded algebra studied in [12, 10]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the triangulated category is not naturally the derived category of an abelian category. The existence of stability conditions, however, gives many such abelian categories, as predicted by mirror symmetry.