论文标题
关于Tori的同源镜对称性的备注
Remarks on the homological mirror symmetry for tori
论文作者
论文摘要
让我们考虑一个$ n $ - 二维复杂的圆环$ t^{2n} _ {j = t}：= \ mathbb {c}^n/2π（\ Mathbb {z}^n \ oplus t \ oplus t \ mathbb {z}^n）$。在这里，$ t $是订单$ n $的复杂矩阵，其虚构零件是积极的。特别是，当我们考虑$ n = 1 $的情况时，通过使用$ - \ frac {1} {t} $或$ t $来定义$ t^2_ {j = t} $的镜像合作伙伴的复杂符号形式。但是，如果我们假设$ n \ geq 2 $，而$ t $是一个单数矩阵，则无法定义$ t^{2n} _ {j = t} $的镜像合作伙伴作为$ n = 1 $的自然概括。在本文中，我们提出了一种避免此问题的方法，并讨论同源镜对称性。
Let us consider an $n$-dimensional complex torus $T^{2n}_{J=T}:=\mathbb{C}^n/2π(\mathbb{Z}^n \oplus T\mathbb{Z}^n)$. Here, $T$ is a complex matrix of order $n$ whose imaginary part is positive definite. In particular, when we consider the case $n=1$, the complexified symplectic form of a mirror partner of $T^2_{J=T}$ is defined by using $-\frac{1}{T}$ or $T$. However, if we assume $n \geq 2$ and that $T$ is a singular matrix, we can not define a mirror partner of $T^{2n}_{J=T}$ as a natural generalization of the case $n=1$ to the higher dimensional case. In this paper, we propose a way to avoid this problem, and discuss the homological mirror symmetry.
