English

On Edge's correspondence associated with \cdot 222

Algebraic Geometry 2017-09-15 v2

Abstract

We describe explicitly the correspondence of Edge between the set of planes contained in the Fermat cubic 4-fold in characteristic 2, and the set of lattice points T of the Leech lattice such that OABT is a regular tetrahedron, where O is the origin of the Leech lattice, and A and B are fixed points of the Leech lattice such that OAB is a regular triangle of edge length 2. Using this description, we present Conway's isomorphism from PSU(6,4) to \cdot 222 in terms of matrices.

Cite

@article{arxiv.1708.06054,
  title  = {On Edge's correspondence associated with \cdot 222},
  author = {Ichiro Shimada},
  journal= {arXiv preprint arXiv:1708.06054},
  year   = {2017}
}

Comments

I corrected the matrix \tilde{\alpha} in Figure 3.1

R2 v1 2026-06-22T21:19:06.058Z