On Hilbert modular threefolds of discriminant 49

2011/08/08 by Lev Borisov, Borisov, Lev A., Paul E. Gunnells +1 · 1 citation
Mathematics · #11F41 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1108.1820

openalex publication_date 2011/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let K be the totally real cubic field of discriminant 49, let O be its ring of integers, and let p be the prime over 7. Let Gamma (p)⊂ Gamma = SL₂(O) be the principal congruence subgroup of level p. This paper investigates the geometry of the Hilbert modular threefold attached to Gamma (p) and some related varieties. In particular, we discover an octic in P³ with 84 isolated singular points of type A₂.

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