Convergence of Hermitian-Yang-Mills connections on two-dimensional Kahler tori and mirror symmetry
Convergence of Hermitian-Yang-Mills connections on two-dimensional Kahler tori and mirror symmetry
复制标题
二维卡勒环面和镜像对称上 Hermitian-Yang-Mills 连接的收敛性
DOI：
10.1007/s11005-021-01405-1
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发表时间：
2021
影响因子：
1.2
通讯作者：
Takeo Nishinou
中科院分区：
文献类型：
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作者：
Takeo Nishinou;Takeo Nishinou
研究了当度量退化时，一族Hermitian-Yang-Mills联络在复二维Kähler环面上的行为。我们证明了这个族的联络的一个收敛定理。根据这一结果和来自镜像对称性的思想，我们在镜像环面上构造了一个(特殊的)拉格朗日子流形。推测这给出了Fukaya的同调镜像对称结构的逆(J Algebraic Geom11(3)：393-512,2002)。
We study the behavior of a family of Hermitian–Yang–Mills connections on complex two-dimensional Kähler tori, when the metrics degenerate. We prove a convergence theorem of connections for this family. From this result and an idea coming from mirror symmetry, we construct a (special) Lagrangian submanifold on the mirror torus. Conjecturally this gives the inverse of the homological mirror symmetry construction of Fukaya (J Algebraic Geom 11(3):393–512, 2002).