A three dimensional ball quotient
Abstract
In connection with our previous investigation about Siegel threefolds which admit a CalabiYau model, we consider ball quotients which belong to the unitary group $\U(1,3)$. 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 $B_i$ of weight one and ten modular forms $C_j$ of weight 2. Both will appear as Borcherds products. We determine the ideal of relations. The forms $C_i$ are cuspidal. Their squares define holomorphic differential forms on the nonsingular models.
 Publication:

arXiv eprints
 Pub Date:
 December 2011
 arXiv:
 arXiv:1201.0131
 Bibcode:
 2012arXiv1201.0131F
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory
 EPrint:
 35 pages