A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact Kähler threefolds

Abstract

We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kähler threefolds. The equation could be thought of as a generalization of the Hitchin equation on Riemann surfaces to Kähler threefolds. In the appendix of arXiv:0805.2192, following an analogy with the Hitchin equation, we introduced a stability condition for a pair consisting of a locally-free sheaf over a compact Kähler threefold and a section of the associated sheaf of the endomorphisms tensored by the canonical bundle of the threefold. In this article, we prove a Hitchin--Kobayashi-type correspondence for this and the Donaldson-Thomas instanton on compact Kähler threefolds.

This paper has been withdrawn. The result of this paper turned out to be a special case of those obtained by Alvarez-Consul and Garcia-Prada. The statement and some description of this paper appear in Appendix of arXiv:0805.2192v3

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• A weak compactness theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
• On the moduli space of Donaldson-Thomas instantons
• A removal singularity theorem of the Donaldson-Thomas instantons on compact Kähler threefolds