Cubic threefolds moduli and the Monster group

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.

arXiv commentThe paper now comes in two parts: Part 1 contains the proof of the main theorem, but depends on some properties of the moduli space of cubic threefolds. These properties are established in Part 2, which is independent of Part 1. Mathematical correctness has been checked by Claude