Postnikov-stability versus semistability of sheaves. (English) Zbl 1318.14017

Hein, Georg; Ploog, David

Asian J. Math. 18, No. 2, 247-262 (2014).

The paper under review generalizes earlier results of the authors obtained in the surface case (see [Int. J. Math. 23, No. 2, Article ID 1250048, 20 p. (2012; Zbl 1239.14009)]).
More precisely, the authors propose a new notion of stability of objects in a triangulated category. This stability depends on the choice of the so called Postnikov-datum, consisting of a Postnikov system and a certain set of integers. The authors show that this new stability generalizes (in all dimensions) both slope semistability and Gieseker semistability and it is preserved by the Fourier-Mukai transforms. They use this stability to construct new compactifications of the moduli space of stable bundles via certain complexes.

Reviewer: Adrian Langer (Warszawa)

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14D20	Algebraic moduli problems, moduli of vector bundles
14J60	Vector bundles on surfaces and higher-dimensional varieties, and their moduli

Keywords:

stable complexes; triangulated category; moduli spaces; Postnikov system

Citations:

Zbl 1239.14009