• DOI:10.1142/S0129167X1100732X
• Corpus ID: 1605444

The geometry and arithmetic of a Calabi-Yau Siegel threefold

@article{Cynk2010TheGA,
  title={The geometry and arithmetic of a Calabi-Yau Siegel threefold},
  author={Sławomir Cynk and Eberhard Freitag and Riccardo Salvati Manni},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}

• S. Cynk, E. Freitag, R. Manni
• Published 18 April 2010
• Mathematics
• arXiv: Algebraic Geometry

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.