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.

We give more details about the stratification of the moduli space of stable cubic threefolds (in Section 4). We also give a simplified (and more detailed) treatment of the central construction of the reflection cover whose covering group is the Bimonster (in Section 5). Section 6 (which was independent of the rest) has been removed and will be published separately