Introduction to stability conditions

Abstract

Let X be a smooth projective Calabi–Yau variety over C. Then Db(X), the derived category of coherent sheaves on X, is equivalent to the category of D-branes on X [9]. In [10], Douglas defined a notion of stability for D-branes on X called Π -stability. This notion of stability was meant to pick out BPS-branes on X. In [7], Bridgeland aimed to define a notion of stability directly for objects in Db(X) which would correspond to Π -stability for D-branes. Bridgeland’s stability can be defined on any triangulated category, and hence has been studied in other cases, such as for varieties which are not Calabi–Yau.