Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stability of vector bundles with twisted sections and the
  Donaldson-Thomas instantons on compact K\"{a}hler threefolds   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.

6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc