Asian Journal of Mathematics

Volume 18 (2014)

Number 2

Postnikov-stability versus semistability of sheaves

Pages: 247 – 262

DOI: http://dx.doi.org/10.4310/AJM.2014.v18.n2.a4

Authors

Georg Hein (Universität Duisburg-Essen, Essen, Germany)

David Ploog (Leibniz-Universität Hannover, Germany)

Abstract

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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