Deformation Theory of Deformed Hermitian Yang?Mills Connections and Deformed Donaldson?Thomas Connections
Deformation Theory of Deformed Hermitian Yang?Mills Connections and Deformed Donaldson?Thomas Connections
复制标题
变形Hermitian Yang?Mills连接和变形Donaldson?Thomas连接的变形理论
DOI：
10.1007/s12220-022-00898-z
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发表时间：
2022
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
变形Donaldson-Thomas（dDT）联络是流形X上的厄米特线丛满足一定非线性偏微分方程的厄米特联络。这被认为是在镜像对称的背景下的（共）结合环的镜像。dDT联络是最近被广泛研究的变形厄米杨-米尔斯（dHYM）联络的一个类似物。本文研究了dDT和dHYM联络的模空间。在前半部分，我们证明了dDT连接的变形是由一个子复形的典范复杂，一个椭圆形的复杂的Reyes Carrión定义，通过引入一个新的coclosused结构。如果变形是通畅的，我们还表明，连通的模空间的分支是a-维环面，其中是第一贝蒂数的X。给出了模空间上的一个正则定向。我们还证明了，如果我们扰动的结构一般在一些假设下，变形的障碍消失。在后半部分，我们证明了dHYM联络的模空间，如果它是非空的，是a维环面，特别是，它是连通的和可定向的。我们还证明了存在一个家庭的模空间沿着变形的基础结构，如果两个上同调类消失。
A deformed Donaldson–Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a-manifoldXsatisfying a certain nonlinear PDE. This is considered to be the mirror of a (co)associative cycle in the context of mirror symmetry. The dDT connection is an analogue of a deformed Hermitian Yang–Mills (dHYM) connection which is extensively studied recently. In this paper, we study the moduli spaces of dDT and dHYM connections. In the former half, we prove that the deformation of dDT connections is controlled by a subcomplex of the canonical complex, an elliptic complex defined by Reyes Carrión, by introducing a new coclosed-structure. If the deformation is unobstructed, we also show that the connected component of the moduli space is a-dimensional torus, whereis the first Betti number ofX. A canonical orientation on the moduli space is also given. We also prove that the obstruction of the deformation vanishes if we perturb the-structure generically under some assumptions. In the latter half, we prove that the moduli space of dHYM connections, if it is nonempty, is a-dimensional torus, especially, it is connected and orientable. We also prove the existence of a family of moduli spaces along a deformation of underlying structures if two cohomology classes vanish.