A three dimensional ball quotient
Algebraic Geometry
2012-01-04 v1 Number Theory
Abstract
In connection with our previous investigation about Siegel threefolds which admit a Calabi--Yau model, we consider ball quotients which belong to the unitary group . In this paper we determine a very particular example of a Picard modular variety of general type. Really we determine the ring of modular forms. This algebra has 25 generators, 15 modular forms of weight one and ten modular forms of weight 2. Both will appear as Borcherds products. We determine the ideal of relations. The forms are cuspidal. Their squares define holomorphic differential forms on the non-singular models.
Cite
@article{arxiv.1201.0131,
title = {A three dimensional ball quotient},
author = {Eberhard Freitag and Riccardo Salvati Manni},
journal= {arXiv preprint arXiv:1201.0131},
year = {2012}
}
Comments
35 pages