标题： 环面泊松流形的膜量子化 显示英文标题

标题： Brane quantization of toric Poisson varieties

摘要： 在本文中，我们提出了紧致Kähler流形与复射影代数簇之间关系的非交换推广。 从一个预量子化的Kähler结构出发，我们使用一个全纯Poisson张量将底层复结构变形为广义复结构，使得预量子线丛及其张量幂变形为一系列广义复膜。 通过计算这些膜之间的同态，我们得到一个齐次坐标环的非交换变形。 作为概念验证，这在所有配备有R矩阵全纯Poisson结构的紧致环面Kähler流形上实现，结果可以称为非交换环面变量。 为了定义广义复膜之间的同态，我们提出了一种方法，该方法涉及将每对广义复膜提升到底层Poisson结构的实辛群胚中的单个共拉格朗日A膜，并计算拉格朗日恒等双截面与提升的共拉格朗日膜之间的A模型中的同态。 这是通过群胚的乘法全纯拉格朗日极化来完成的。 显示英文摘要

摘要： In this paper we propose a noncommutative generalization of the relationship between compact K\"ahler manifolds and complex projective algebraic varieties. Beginning with a prequantized K\"ahler structure, we use a holomorphic Poisson tensor to deform the underlying complex structure into a generalized complex structure, such that the prequantum line bundle and its tensor powers deform to a sequence of generalized complex branes. Taking homomorphisms between the resulting branes, we obtain a noncommutative deformation of the homogeneous coordinate ring. As a proof of concept, this is implemented for all compact toric K\"ahler manifolds equipped with an R-matrix holomorphic Poisson structure, resulting in what could be called noncommutative toric varieties. To define the homomorphisms between generalized complex branes, we propose a method which involves lifting each pair of generalized complex branes to a single coisotropic A-brane in the real symplectic groupoid of the underlying Poisson structure, and compute morphisms in the A-model between the Lagrangian identity bisection and the lifted coisotropic brane. This is done with the use of a multiplicative holomorphic Lagrangian polarization of the groupoid.