紧Kähler三重上具有扭截面的向量丛和Donaldson-Thomas瞬子的稳定性
A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact Kähler threefolds
摘要：
我们考虑一个版本的厄米-爱因斯坦方程，但扰动的希格斯场的解决方案称为唐纳森-托马斯瞬子紧凑凯勒三倍。该方程可以被认为是黎曼曲面上的希钦方程到凯勒三重曲面的推广。在arXiv：0805.2192的附录中，我们引入了一个与希钦方程类似的稳定性条件，该条件适用于由紧Kähler三重上的局部自由层和由三重的典范丛张紧的自同态的相关层的一部分组成的对。在这篇文章中，我们证明了一个Hitchin-Kobayashi型对应，这和Donaldson-Thomas瞬子紧Kähler三倍。
英文摘要：
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.
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