Eggs in finite projective spaces and unitals in translation planes
Combinatorics
2023-01-10 v1
Abstract
Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the Andr\'e/Bruck-Bose representation of translation planes of dimension at most two over their kernel, and since eggs of PG(4m-1,q), m>=1, are a generalization of ovoids, we explore the relation between eggs and unitals in translation planes of higher dimension over their kernel. By investigating such a relationship, we construct a unital in the Dickson semifield plane of order 3^{10}, which is represented in PG(20,3) by a cone whose base is a set of points constructed from the dual of the Penttila-Williams egg in PG(19,3). This unital is not polar; so, up to the knowledge of the authors, it seems to be a new unital in such a plane.
Keywords
Cite
@article{arxiv.2301.03059,
title = {Eggs in finite projective spaces and unitals in translation planes},
author = {Giusy Monzillo and Tim Penttila and Alessandro Siciliano},
journal= {arXiv preprint arXiv:2301.03059},
year = {2023}
}