A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact K\"{a}hler 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 K\"ahler threefolds. The equation could be thought of as a generalization of the Hitchin equation on Riemann surfaces to K\"ahler 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 K\"ahler 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 K\"ahler threefolds.
Keywords
Cite
@article{arxiv.1306.5590,
title = {A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact K\"{a}hler threefolds},
author = {Yuuji Tanaka},
journal= {arXiv preprint arXiv:1306.5590},
year = {2013}
}
Comments
This paper has been withdrawn.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