Postnikov-stability versus semistability of sheaves (Q407357)

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)]).NEWLINENEWLINEMore 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.