Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Siegel Threefolds with a Calabi-Yau Model II

  • Received : 2011.04.24
  • Accepted : 2011.07.05
  • Published : 2013.06.23
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Abstract

In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety $\mathcal{X}$ that is the complete intersection of four quadrics in $\mathbb{P}^7(\mathbb{C})$. This is biholomorphic equivalent to the Satake compactification of $\mathcal{H}_2/{\Gamma}^{\prime}$ for a certain subgroup ${\Gamma}^{\prime}{\subset}Sp(2,\mathbb{Z})$ and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold $\tilde{\mathcal{X}}$. Then we will consider the action of quotients of modular groups on $\mathcal{X}$ and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.

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References

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