Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
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环面 Calabi-Yau 超曲面的环面态射和纤维化
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
S. Yau
中科院分区：
文献类型：
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作者：
Y. Hu;Chien‐Hao Liu;S. Yau
物理学家已经使用了环曲面类型的特殊纤维，例如Candelas学派，在Het/F理论对偶性的研究中构建对偶对。受此启发，我们在本文中研究了环面变体之间环面态射的细节。特别是，给出了纤维的完整复曲面描述（通用和非通用纤维）、图像以及复曲面态射的扁平化分层。提供了两个例子来说明讨论。然后我们转向研究环面态射对环面超曲面的限制。其细节可以通过具有定义超曲面的截面的线束的各种限制来理解。这些一般的环面几何讨论提出了环面态射和其中环面超曲面的诱发纤维化的细节的计算方案。我们应用这个方案来研究 Braun-Candelas-dlOssa-Grassi 最近的工作中出现的 4 维椭圆 Calabi-Yau toric 超曲面族。提供了用于计算的 Maple 代码。最后列出了未来工作的一些方向。
Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms between toric varieties. In particular, a complete toric description of fibers - both generic and non-generic -, image, and the flattening stratification of a toric morphism are given. Two examples are provided to illustrate the discussions. We then turn to the study of the restriction of a toric morphism to a toric hypersurface. The details of this can be understood by the various restrictions of a line bundle with a section that defines the hypersurface. These general toric geometry discussions give rise to a computational scheme for the details of a toric morphism and the induced fibration of toric hypersurfaces therein. We apply this scheme to study the family of 4-dimensional elliptic Calabi-Yau toric hypersurfaces that appear in a recent work of Braun-Candelas-dlOssa-Grassi. The Maple codes that are employed for the computation are provided. Some directions for future work are listed in the end.