The geometry and arithmetic of a Calabi-Yau Siegel threefold

Slawomir Cynk; Eberhard Freitag; Riccardo Salvati Manni

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arXiv · 1004.2997

The geometry and arithmetic of a Calabi-Yau Siegel threefold

Slawomir Cynk·Eberhard Freitag·Riccardo Salvati Manni

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Abstract

In this paper we treat in details a modular variety $\cal Y$ that has a Calabi-Yau model, $\tilde{\cal Y}$. We shall describe the structure of the ring of modular forms and its geometry. We shall illustrate two different methods of producing the Hodge numbers. The first uses the definition of $\cal Y$ as the quotient of another known Calabi-Yau variety. In this case we will get the Hodge numbers considering the action of the group on a crepant resolution $\tilde{\cal X}$ of $\cal X$. The second, purely algebraic geometric, uses the equations derived from the ring of modular forms and is based on determining explicitly the Calabi-Yau model $\tilde{\cal Y}$ and computing the Picard group and the Euler characteristic.

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Slawomir Cynk, Eberhard Freitag, Riccardo Salvati Manni. 2010-04-18. The geometry and arithmetic of a Calabi-Yau Siegel threefold. https://arxiv.org/abs/1004.2997

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