论文标题
deligne的猜想和镜子对称性
Deligne's conjecture and mirror symmetry
论文作者
论文摘要
在本文中，我们将研究Calabi-yau三倍的镜像对称性与Deligne对关键动机的特殊值的猜想。使用镜子对称的理论，我们将开发一种方法，以计算单参数镜对的镜像家族中的calabi-yau时期三倍。我们将举两个示例以说明这种方法的工作原理，我们将根据三个形式的经典时期来表达deligne的时期。使用这种方法，我们将计算Candelas，de la Ossa，Elmi和van Straten最近的一篇论文中研究的Calabi-yau三倍的deligne时期。根据它们的数值结果，我们将明确表明该卡拉比（Calabi-Yau）三倍满足Deligne的猜想。本文的第二个目的是向物理界介绍deLigne的猜想，并提供进一步的证据，表明物理学与数字理论之间可能存在有趣的联系。
In this paper, we will study the connections between the mirror symmetry of Calabi-Yau threefolds and Deligne's conjecture on the special values of the $L$-functions of critical motives. Using the theory of mirror symmetry, we will develop a method to compute the Deligne's period for a Calabi-Yau threefold in the mirror family of a one-parameter mirror pair. We will give two examples to show how this method works, and we will express the Deligne's period in terms of the classical periods of the threeform. Using this method, we will compute the Deligne's period of a Calabi-Yau threefold studied in a recent paper by Candelas, de la Ossa, Elmi and van Straten. Based on their numerical results, we will explicitly show that this Calabi-Yau threefold satisfies Deligne's conjecture. A second purpose of this paper is to introduce the Deligne's conjecture to the physics community, and provide further evidence that there might exist interesting connections between physics and number theory.
