The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design
Combinatorics
2024-02-13 v1
Abstract
A conic of the Veronese surface in PG(5,3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model for Witt's 5- design, the blocks being the hyperplane sections containing more than three (actually six) points of . As such a point model is projectively unique, the present construction yields an easy coordinate-free approach to some results obtained independently by H.S.M. Coxeter and G. Pellegrino, including a projective representation of the Mathieu group in PG(5,3).
Keywords
Cite
@article{arxiv.1210.2055,
title = {The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design},
author = {Hans Havlicek},
journal= {arXiv preprint arXiv:1210.2055},
year = {2024}
}
Comments
Research supported by the Austrian FWF, project P12353--MAT