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Stability manifolds of P1 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( P1 ) of coherent sheaves on P1 , denoted by Stab(D( P1 )). 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 P1 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 O 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 . ^
"Stability manifolds of P1 and Calabi-Yau surfaces"
(January 1, 2006).
Electronic Doctoral Dissertations for UMass Amherst.