论文标题
符号群集歧管的封闭弦镜
Closed string mirrors of symplectic cluster manifolds
论文作者
论文摘要
对于Maslov的基本$ b $，$ 0 $ lagrangian的圆环纤维带有奇异性，将支架分配给每个$ p \ subset b $，相对符号共生共同体学位为$ 0 $ 0 $。我们计算了在四个维符号群集歧管上的淋巴结拉格朗日圆环纤维纤维的捆绑。我们表明，这是在非架构的圆环纤维化下某个刚性分析空间的结构捆扎的推动力。刚性的分析空间是从相对sheaf的规范方式构造的，被称为\ emph {封闭的弦乐镜}。该结构通过应用一般的公理特性而不是全体形态曲线的临时分析来依赖于局部模型的计算相对SH。这些公理特性包括先前确定的属性，例如Mayer-Vietoris特性和用于完整嵌入的位置；以及诸如Hartogs属性和相对$ SH $的墙壁交叉的全体形态卷的保存属性等新的。我们指出了适用相同技术的一些较高维度设置。
For the base $B$ of a Maslov $0$ Lagrangian torus fibration with singularities consider the sheaf assigning to each $P\subset B$ the relative symplectic cohomology in degree $0$ of its pre-image. We compute this sheaf for nodal Lagrangian torus fibrations on four dimensional symplectic cluster manifolds. We show that it is the pushforward of the structure sheaf of a certain rigid analytic space under a non-archimedean torus fibration. The rigid analytic space is constructed in a canonical way from the relative SH sheaf and is referred as the \emph{closed string mirror}. The construction relies on computing relative SH for local models by applying general axiomatic properties rather than ad hoc analysis of holomorphic curves. These axiomatic properties include previously established ones such as the Mayer-Vietoris property and locality for complete embeddings; and new ones such as the Hartogs property and the holomorphic volume form preservation property of wall crossing in relative $SH$. We indicate some higher dimensional settings where the same techniques apply.
