Some Siegel Threefolds with a Calabi-Yau Model II

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 2,  2013, pp.149-174
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.2.149
Title & Authors
Some Siegel Threefolds with a Calabi-Yau Model II
Freitag, Eberhard; Manni, Riccardo Salvati;

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 $\small{\mathcal{X}}$ that is the complete intersection of four quadrics in $\small{\mathbb{P}^7(\mathbb{C})}$. This is biholomorphic equivalent to the Satake compactification of $\small{\mathcal{H}_2/{\Gamma}^{\prime}}$ for a certain subgroup $\small{{\Gamma}^{\prime}{\subset}Sp(2,\mathbb{Z})}$ 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 $\small{\tilde{\mathcal{X}}}$. Then we will consider the action of quotients of modular groups on $\small{\mathcal{X}}$ and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.
Keywords
Calabi-Yau;Siegel modular varieties;
Language
English
Cited by
1.
On the converse theorem for Borcherds products, Journal of Algebra, 2014, 397, 315
2.
On isomorphisms between Siegel modular threefolds, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2016, 86, 1, 55
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