论文标题
颤抖代数堆栈的镜子对称性
Mirror Symmetry for Quiver Algebroid Stacks
论文作者
论文摘要
在本文中，我们提供了Quiver代数堆栈和相关的镜像函数的新结构，以进行符号歧管。首先，我们制定了颤抖堆栈的概念，箭量堆栈是通过将多个颤动代数粘合在一起而形成的几何结构。接下来，我们为Quiver stacks开发了$ a_ \ infty $类别的表示理论。主要思想是将$ a_ \ infty $类别扩展到Quiver堆叠的NC构造对象的集合。该扩展名涉及非平凡的GERBE术语。它赋予了符号几何形状的应用，该几何形状通过镜像对称性桥接了带轮的研究和表示理论。 我们提供了一个构造镜颤动堆栈的一般框架。特别是，我们开发了一种新颖的方法来粘合拉格朗日，通过使用“全球中间代理”的准同态彼此脱节，这是一种lagrangans的沉浸式，产生了镜子颤动。该方法从根本上依赖于使用颤抖的堆栈。我们在刺穿的椭圆曲线中进行了紧凑型浸入式拉格朗日的结构，从而产生了镜子NC局部投影平面。
In this paper, we provide a new construction of quiver algebroid stacks and the associated mirror functors for symplectic manifolds. First, we formulate the concept of a quiver stack, which is a geometric structure formed by gluing multiple quiver algebras together. Next, we develop a representation theory of $A_\infty$ categories by quiver stacks. The main idea is to extend the $A_\infty$ category over a quiver stack of a collection of nc-deformed objects. The extension involves non-trivial gerbe terms. It gives an application of symplectic geometry that bridges the study of sheaves and representation theory through mirror symmetry. We provide a general framework for constructing mirror quiver stacks. In particular, we develop a novel method of gluing Lagrangians which are disjoint from each other by using quasi-isomorphisms with a `global middle agent', which is a Lagrangian immersion that produces a mirror quiver. The method relies fundamentally on the use of quiver stacks. We carry out this construction for compact immersed Lagrangians in a punctured elliptic curve, which results in a mirror nc local projective plane.
