关于Donaldson-Thomas瞬子的模空间
On the moduli space of Donaldson-Thomas instantons
摘要：
与Donaldson和Thomas [DT]的一个程序相一致，Thomas [Th]通过使用代数几何技术，从（半）稳定层的模空间构造了光滑投射Calabi-Yau三重的变形不变量，现在称为Donaldson-Thomas不变量。在同一文件[Th]，托马斯指出，某些扰动厄米-爱因斯坦方程可能会产生一个分析理论的不变。本文建立了辛6-流形上的方程，并给出了由方程导出的模空间的局部模型和结构。然后，我们描述了一个Hitchin-Kobayashi风格的对应紧凑的Kähler三倍，这原来是一个特殊的情况下，结果由Alvarez-Consul和Garcia-Prada [AG]的方程。
英文摘要：
In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of (semi-)stable sheaves by using algebraic geometry techniques. In the same paper [Th], Thomas noted that certain perturbed Hermitian-Einstein equations might possibly produce an analytic theory of the invariant. This article sets up the equations on symplectic 6-manifolds, and gives the local model and structures of the moduli space coming from the equations. We then describe a Hitchin-Kobayashi style correspondence for the equations on compact Kähler threefolds, which turns out to be a special case of results by Alvarez-Consul and Garcia-Prada [AG].
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