Postnikov-stability versus semistability of sheaves

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable sheaves. As one application we compactify a moduli space of stable bundles using genuine complexes via Fourier-Mukai transforms.

Keywords

stable complexes, derived category, moduli spaces, Postnikov stability

2010 Mathematics Subject Classification

14D20, 14F05, 14J60

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Published 13 May 2014