English

Cubic threefolds moduli and the Monster group

Algebraic Geometry 2024-11-27 v2 Group Theory

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.

Keywords

Cite

@article{arxiv.2310.20124,
  title  = {Cubic threefolds moduli and the Monster group},
  author = {Eduard Looijenga},
  journal= {arXiv preprint arXiv:2310.20124},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T13:06:52.789Z