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Stability manifolds of P(1) and Calabi-Yau surfaces

So Okada, University of Massachusetts Amherst


The notion of stability conditions on triangulated categories was formulated in [15]. 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 [32]. 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 [15], [23], [32], [28], and [17], higher-dimensional spaces in [35], [14], [16], [12], [13], [28], [29], [2], [36], [24], [7], and [1], and A∞-categories in [35], [34], [37], and [26]. The stability manifold of the category [special characters omitted] for sl2 has been computed in [30]. Some general aspects have been studied in [2] and [23]. The author recommends [11], [3, Section 0.6] and [20], [19], [21] for introductions and the original physical motivation to this subject. Notation of derived categories is mainly based on [22].

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Recommended Citation

Okada, So, "Stability manifolds of P(1) and Calabi-Yau surfaces" (2006). Doctoral Dissertations Available from Proquest. AAI3242109.