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arXiv · 1306.5590

A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact K\"{a}hler threefolds

Yuuji Tanaka
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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.

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Yuuji Tanaka. 2013-06-24. A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact K\"{a}hler threefolds. https://arxiv.org/abs/1306.5590

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