Quotients of Hypersurfaces in Weighted Projective Space

Details Quotients of Hypersurfaces in Weighted Projective Space Quotients of Hypersurfaces in Weighted Projective Space

2009-05-13

arxiv.org/abs/0905.2099v1

Mathematics

Algebraic Geometry

Scientific paper

In [1] some quotients of one-parameter families of Calabi-Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let $A$ be an invertible matrix with non-negative integer entries. We introduce varieties $X_A$ and $\overline{M}_A$ in weighted projective space and in ${\mathbb P}^n$, respectively. The variety $\overline{M}_A$ turns out to be a quotient of a Fermat variety by a finite group. As a by-product, $X_A$ is a quotient of a Fermat variety and $\overline{M}_A$ is a quotient of $X_A$ by a finite group. We apply this construction to some families of Calabi-Yau manifolds in order to show their birationality.

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