Quantum Cohomology and Closed-String Mirror Symmetry for Toric Varieties
Quantum Cohomology and Closed-String Mirror Symmetry for Toric Varieties
复制标题
DOI：
10.1093/qmathj/haz056
复制
发表时间：
2018-02
期刊：
影响因子：
--
通讯作者：
Jack Smith
中科院分区：
文献类型：
--
作者：
Jack Smith
我们给出了一个简短的新的计算的量子上同调的任意光滑（半投射）环面品种$X$，直接显示Kodaira-Spencer映射的aya-Oh-Ohta-Ono定义同构到一个合适的雅可比环。与以前的这类结果相反，$X$不必是紧的。证明是基于纯粹的代数事实，一类广义雅可比环相关联的$X$是免费的模块上的诺维科夫环。当$X$是单调的介绍，我们得到的是完全明确的，只使用众所周知的计算与标准复杂的结构。
We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety $X$, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono defines an isomorphism onto a suitable Jacobian ring. In contrast to previous results of this kind, $X$ need not be compact. The proof is based on the purely algebraic fact that a class of generalized Jacobian rings associated to $X$ are free as modules over the Novikov ring. When $X$ is monotone the presentation we obtain is completely explicit, using only well-known computations with the standard complex structure.