Cubic threefolds moduli and the Monster group

2023/10/31 by Eduard Looijenga, Looijenga, Eduard
Mathematics · #14D23 #20D08 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2310.20124

openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Allcock constructed a 13-dimensional complex ball quotient of which he conjectured that it admits a natural covering with covering group isomorphic to the Bimonster. This ball quotient contains the moduli space of cubic threefolds as an open dense subset of a 10-dimensional complex subball quotient. We prove that this subball quotient has a neighborhood in the Allcock ball quotient over which the conjectured cover exists.

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