论文标题
量子（非共同）曲折的几何形状：基础
Quantum (Non-commutative) Toric Geometry: Foundations
论文作者
论文摘要
在本文中，我们将引入量子曲折的品种，这些品种（非交通）对普通的曲折品种进行了概括，在这些品种中，经典理论的所有摩尔犬都被量子托里所取代。量子折叠的几何形状是经典理论的非共同版本。它在非通知的大多数定理和曲折几何学的特性上概括了。通过将量子曲折品种视为（非代数）堆栈，我们定义了它们的类别，并表明它等同于量子风扇的类别。我们开发了量子几何不变理论（QGIT）类型的量子旋转品种的构造。 与经典的感谢您的品种不同，量子圆环品种接收模量，我们定义了它们的模量空间，证明这些空间是Orbifolds，并且在有利的情况下，直到均匀的情况下，它们都承认了一个复杂的结构。
In this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the non-commutative version of the classical theory; it generalizes non-trivially most of the theorems and properties of toric geometry. By considering quantum toric varieties as (non-algebraic) stacks, we define their category and show that it is equivalent to a category of quantum fans. We develop a Quantum Geometric Invariant Theory (QGIT) type construction of Quantum Toric Varieties. Unlike classical toric varieties, quantum toric varieties admit moduli and we define their moduli spaces, prove that these spaces are orbifolds and, in favorable cases, up to homotopy, they admit a complex structure.
