Stability manifolds of P(1) and Calabi-Yau surfaces
The notion of stability conditions on triangulated categories was formulated in . It organizes certain bounded t-structures on a triangulated category into a complex manifold.
We will describe the stability manifold of the bounded derived category D([special characters omitted]) of coherent sheaves on [special characters omitted], denoted by Stab(D([special characters omitted])). This part of the work has been published in .
After preparation on spectral sequences and n-Calabi-Yau categories , we will concentrate on stability conditions on 2-Calabi-Yau categories. Our main result here is the connectedness of stability manifolds of the cotangent bundle of [special characters omitted] and abelian surfaces. This completes Bridgeland's work on the description of these manifolds.
Stability conditions have been studied for one-dimensional spaces in , , , , and , higher-dimensional spaces in , , , , , , , , , , , and , and A∞-categories in , , , and . The stability manifold of the category [special characters omitted] for sl2 has been computed in . Some general aspects have been studied in  and .
The author recommends , [3, Section 0.6] and , ,  for introductions and the original physical motivation to this subject. Notation of derived categories is mainly based on .