Mirror quintics, discrete symmetries and Shioda maps
Mirror quintics, discrete symmetries and Shioda maps
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镜像五次方程、离散对称性和 Shioda 映射
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Tyler L. Kelly
中科院分区：
文献类型：
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作者：
G. Bini;B. Geemen;Tyler L. Kelly
在最近的一篇论文中，Doran， Greene和Judes考虑了具有有限对称群的五次三重的一个参数族。一个令人惊讶的结果是，这六个族中的每一个都有相同的与全纯3型相关的皮卡德-富克斯方程。在本文中，我们给出了一个简单的论证，涉及到镜像五项族，它隐含了这个结果。利用Shioda构造，我们还将这些单参数族的某些商与镜像五项族联系起来。我们的构造推广到（n-1）维射影空间中的n次Calabi Yau变换。
In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the holomorphic 3-form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi Yau varieties in (n-1)-dimensional projective space.