A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list
A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list
复制标题
DOI：
10.1007/jhep02(2015)158
复制
发表时间：
2014-11
影响因子：
5.4
通讯作者：
Ross Altman;J. Gray;Yang-Hui He;Vishnu Jejjala;B. Nelson
中科院分区：
文献类型：
--
作者：
Ross Altman;J. Gray;Yang-Hui He;Vishnu Jejjala;B. Nelson
Kreuzer和Skarke通过提供四维b[1]中存在的所有473,800,776个反射多面体的完整结构，以创建已知最大的Calabi-Yau三倍数据库而闻名。这些多面体描述了环境环面变体的奇异极限，其中Calabi-Yau三折可以作为超曲面存在。在本文中，我们回顾了如何使用环状结构提取Calabi-Yau三倍体的拓扑和几何信息，并提供了一个在线数据库（参见http://nuweb1）。神经膜。Edu/cydatabase)，物理学家感兴趣的这些量的详细清单。许多由Kreuzer-Skarke表描述的奇异环境空间可以被平滑成多个不同的环形环境空间，描述不同的Calabi-Yau三倍。我们提供了一个不同的Calabi-Yau三倍的列表，可以从每个多面体中获得，直到当前的计算限制。然后，除了Hodge数据外，我们还提供了与这些Calabi-Yau相关的各种数量的详细信息，如chen类、交集数、Kähler和Mori锥。这些数据为Kreuzer-Skarke表的许多物理应用提供了一个有用的起点。
Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions [1]. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://nuweb1. neu. edu/cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the Kähler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list.