Postnikov-Stability versus Semistability of Sheaves

Understand

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.