A three dimensional ball quotient

2011/12/30 by Eberhard Freitag, Freitag, Eberhard, Riccardo Salvati Manni +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1201.0131

35 pages

arxiv created 2011/12/30 · openalex publication_date 2011/12/30 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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 non-singular models.

Related

• The geometry and arithmetic of a Calabi-Yau Siegel threefold
• Vector valued modular forms on three dimensional ball
• Some ball quotients with a Calabi--Yau model
• The Modular Form of the Barth-Nieto Quintic
• Some Siegel threefolds with a Calabi-Yau model II