论文标题
复杂的摩尔比的Gerby变形和同源镜子对称性
A gerby deformation of complex tori and the homological mirror symmetry
论文作者
论文摘要
令$（x，\ check {x}）$为一对复杂的圆环$ x $及其镜子伙伴$ \ check {x} $。这对镜对被描述为琐碎的特殊拉格朗日圆环纤维$ x \ rightarrow b $和$ \ check {x} \ rightarrow b $在同一基本空间$ b $的Syz Construction上。然后，我们可以将lagrangian $ s $ s $ s $ s $ s $ s $ s $ \ \ check {x} \ check {x} \ rightarrow b $ rightarrow b $ rightarrow b $ and rimation local Systems $ MATHAM $ MATHAL的$ s $ S $ e（S，\ Mathcal {l}）\ rymorphic line Bundle $ e（S，\ Mathcal {l}）\将在本文中，我们首先通过某个平坦的Gerbe $ \ Mathcal {Gerbe $ \ Mathcal {g} $及其镜像伙伴$ \ check {x} _ {\ Mathcal {g Mathcal {g}} $（x，x，x，x，x，x，x，x，x，cecks），＆condect） $ e（s，\ mathcal {l}）$和$（s，\ mathcal {l}）$上的变形镜对$ $（x _ {\ mathcal {g}}}，\ check {x} _ {x} _ {\ mathcal {g}}）$。
Let $(X,\check{X})$ be a mirror pair of a complex torus $X$ and its mirror partner $\check{X}$. This mirror pair is described as the trivial special Lagrangian torus fibrations $X\rightarrow B$ and $\check{X}\rightarrow B$ on the same base space $B$ by SYZ construction. Then, we can associate a holomorphic line bundle $E(s,\mathcal{L})\rightarrow X$ to a pair $(s,\mathcal{L})$ of a Lagrangian section $s$ of $\check{X}\rightarrow B$ and a unitary local system $\mathcal{L}$ along it. In this paper, we first construct the deformation $X_{\mathcal{G}}$ of $X$ by a certain flat gerbe $\mathcal{G}$ and its mirror partner $\check{X}_{\mathcal{G}}$ from the mirror pair $(X,\check{X})$, and discuss deformations of objects $E(s,\mathcal{L})$ and $(s,\mathcal{L})$ over the deformed mirror pair $(X_{\mathcal{G}},\check{X}_{\mathcal{G}})$.
