标题： 广义Hirzebruch纤维丛的几何量子化 显示英文标题

标题： Geometric quantization of generalized Hirzebruch fibrations

摘要： 赫兹布吕赫曲面被定义为射影化线丛，其基础空间为$\C\mathbb{P}^1$，支持环作用，因此代表了一类无限多个复维数为 2 的辛环簇流形。本文将构造一类无穷多个环簇流形，它们作为射影丛，其基础空间为$\mathbb{C}\mathbb{P}^d$，并且对于任意复维数$d$，证明每个流形都支持一个辛结构。利用这些流形的环与辛结构，我们研究了它们的几何量子化以及它如何与纤维化扭转参数的不同取值相关联。 显示英文摘要

摘要： Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class of toric manifolds given as projective bundles over $\mathbb{C}\mathbb{P}^d$ will be constructed for every complex dimension $d$ and it will be shown that each manifold supports a symplectic structure. With the toric and symplectic structure of the manifolds at our disposal, we then study their geometric quantization and how it relates to different values of the twisting parameter of the fibrations.