The zeta function of monomial deformations of Fermat hypersurfaces
The zeta function of monomial deformations of Fermat hypersurfaces
复制标题
费马超曲面单项变形的 zeta 函数
DOI：
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发表时间：
2007
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通讯作者：
R. Kloosterman
中科院分区：
文献类型：
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作者：
R. Kloosterman
本文旨在对最近在镜像对称背景下获得的一些品种家族的 zeta 函数结果给出数学解释。在此过程中，我们获得了最近在 P^n 中平滑超曲面上的点计数算法中使用的一些结果的具体且明确的示例。特别是，我们扩展了 Kadir 和 Yui 的单项式动机对应关系，并给出了与费马超曲面单项变形相关的 p 进 Picard-Fuchs 方程的显式解。作为副产品，我们获得了某些奇异仿射簇的刚性上同调的庞加莱对偶性。
This paper intends to give a mathematical explanation for results on the zeta-function of some families of varieties recently obtained in the context of Mirror Symmetry. In doing so, we obtain concrete and explicit examples for some results recently used in algorithms to count points on smooth hypersurfaces in P^n. In particular, we extend the monomial-motive correspondence of Kadir and Yui and we give explicit solutions to the p-adic Picard-Fuchs equation associated with monomial deformations of Fermat hypersurfaces. As a by-product we obtain Poincare Duality for the Rigid cohomology of certain singular affine varieties.