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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Introduction to Stability Conditions
verfasst von : Rebecca Tramel
Erschienen in: Superschool on Derived Categories and D-branes
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Abstract
Let X be a smooth projective Calabi–Yau variety over \(\mathbb {C}\). Then \(\mathcal {D}^b(X)\), 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 \(\Pi \)-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 \(\mathcal {D}^b(X)\) which would correspond to \(\Pi \)-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.