Deformation Theory of Deformed Donaldson?Thomas Connections for $${\text {Spin}(7)}$$-manifolds
Deformation Theory of Deformed Donaldson?Thomas Connections for $${\text {Spin}(7)}$$-manifolds
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变形唐纳森的变形理论？$${ ext {Spin}(7)}$$-流形的托马斯连接
DOI：
10.1007/s12220-021-00712-2
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Yamamoto Hikaru
中科院分区：
文献类型：
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作者：
Kawai Kotaro;Yamamoto Hikaru
具有a-结构的流形的变形Donaldson-Thomas联络（我们称之为a-dDT联络）是由完全非线性偏微分方程定义的具有a-结构的流形上的Hermitian联络。它首先由Lee和Leung作为由真实的Fourier-Mukai变换得到的Cayley循环的镜像对象引入，并且在我们的另一篇论文中提出了它的替代定义。正如名字所示，-dDT连接也可以被认为是唐纳森-托马斯连接（-瞬子）的类似物。在本文中，使用我们的定义，我们表明，模空间的dDT连接有类似的性质，这些对象。也就是说，我们为一个开子集显示以下内容。(1)的元素的变形由Reyes Carrión定义的正则复形的一个子复形控制，通过从初始-结构和一个-dDT联络引入一个新的-结构。(2)期望的维数是有限的。如果初始结构是挠自由的，则它是基流形的第一个Betti数。(3)在一些温和的假设下，是光滑的，如果我们扰动的初始结构一般。(4)如果所有的变形都是无障碍的，则该空间允许正则定向。
A deformed Donaldson–Thomas connection for a manifold with a-structure, which we call a-dDT connection, is a Hermitian connection on a Hermitian line bundleLover a manifold with a-structure defined by fully nonlinear PDEs. It was first introduced by Lee and Leung as a mirror object of a Cayley cycle obtained by the real Fourier–Mukai transform and its alternative definition was suggested in our other paper. As the name indicates, a-dDT connection can also be considered as an analogue of a Donaldson–Thomas connection (-instanton). In this paper, using our definition, we show that the moduli spaceof-dDT connections has similar properties to these objects. That is, we show the following for an open subset. (1) Deformations of elements ofare controlled by a subcomplex of the canonical complex defined by Reyes Carrión by introducing a new-structure from the initial-structure and a-dDT connection. (2) The expected dimension ofis finite. It is, the first Betti number of the base manifold, if the initial-structure is torsion-free. (3) Under some mild assumptions,is smooth if we perturb the initial-structure generically. (4) The spaceadmits a canonical orientation if all deformations are unobstructed.