Calabi-Yau manifolds and mirror symmetry

卡拉比-丘流形和镜像对称

• 批准号: 5247112
• 负责人: Professor Dr. Duco van Straten
• 金额: --
• 依托单位: Arbeitsgruppe Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2004-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5247112?language=en
• 关键词: Calabi; Yau; manifolds; mirror; symmetry

The reflexive polytope construction of Batyrev and the subsequent work of Givental accounts for almost all cases of mirror symmetry that have been worked out so far. In algebraic geometry however, one encounters Calabi-Yau spaces that are not given as complete intersections in toric varieties and a very interesting problem is to find mirror manifolds in these cases, in order to understand how general the mirror symmetry phenomenon is. The plan is to test the range of mirror symmetry by working out more examples, in particular we want to study examples with Picard number one and try to find mirror manifolds. On the mirror side, we seek to construct Calabi-Yau manifolds with small h1,2, for example by imposing singularities, and search their moduli spaces for points of maximal unipotent monodromy.

巴特列夫的自反多面体结构和吉文塔尔随后的工作几乎解释了迄今为止所有的镜像对称情况。然而，在代数几何中，人们会遇到在复曲面簇中没有给出完全相交的卡-丘空间，一个非常有趣的问题是在这些情况下找到镜像流形，以便理解镜像对称现象有多普遍。我们的计划是通过更多的例子来测试镜像对称的范围，特别是我们想研究Picard数为1的例子，并试图找到镜像流形。在镜像方面，我们试图构造具有小h1，2的卡-丘流形，例如通过施加奇点，并在它们的模空间中搜索最大幂单值点。