F理论中的CICY工具
Tools for CICYs in F-theory
摘要：
我们提供了一套工具，用于分析椭圆纤维卡-丘流形的几何形状，从描述的总空间，而不是维尔斯特拉斯模型或指定类型的纤维/基地。这样一种F-理论紧化的方法使得某些通常被隐藏的几何性质显现出来。具体来说，我们回顾了如何在这样的几何隔离genus-one纤维化，然后描述如何找到他们的部分明确。这包括一个完整的参数化的Mordell-Weil组，其中非平凡的。然后，我们描述了如何分析相关的维尔斯特拉斯模型，雅可比矩阵和解决的几何形状。我们说明我们的讨论与具体的例子，这是完全相交的产品的射影空间（CICY）。所提出的例子包括表现出非阿贝尔对称性和更高的秩Mordell-Weil群的情况。我们也在这方面的非平坦纤维化的一些意见。在这篇论文的姊妹篇[1]中，这些结果将被用来分析在已知的卡-丘流形结构中普遍存在的多重纤维化对弦对偶的影响。
英文摘要：
We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fiber/base. Such an approach to the subject of F-theory compactification makes certain geometric properties, which are usually hidden, manifest. Specifically, we review how to isolate genus-one fibrations in such geometries and then describe how to find their sections explicitly. This includes a full parameterization of the Mordell-Weil group where non-trivial. We then describe how to analyze the associated Weierstrass models, Jacobians and resolved geometries. We illustrate our discussion with concrete examples which are complete intersections in products of projective spaces (CICYs). The examples presented include cases exhibiting non-abelian symmetries and higher rank Mordell-Weil group. We also make some comments on non-flat fibrations in this context. In a companion paper [1] to this one, these results will be used to analyze the consequences for string dualities of the ubiquity of multiple fibrations in known constructions of Calabi-Yau manifolds.
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