Characterising elliptic solids of $Q(4,q)$, $q$ even

S. G. Barwick; Alice M. W. Hui; Wen-Ai Jackson

Characterising elliptic solids of $Q(4,q)$, $q$ even

Combinatorics 2019-06-11 v1

Authors: S. G. Barwick , Alice M. W. Hui , Wen-Ai Jackson

Abstract

Let $E$ be a set of solids (hyperplanes) in $PG(4,q)$ , $q$ even, $q>2$ , such that every point of $PG(4,q)$ lies in either $0$ , $\frac12q^3$ or $\frac12(q^3-q^2)$ solids of $E$ , and every plane of $PG(4,q)$ lies in either $0$ , $\frac12q$ or $q$ solids of $E$ . This article shows that $E$ is either the set of solids that are disjoint from a hyperoval, or the set of solids that meet a non-singular quadric $Q(4,q)$ in an elliptic quadric.

Keywords

elliptic solids PG(4,q) hyperoval non-singular quadric elliptic quadric finite geometry

Cite

@article{arxiv.1906.03985,
  title  = {Characterising elliptic solids of $Q(4,q)$, $q$ even},
  author = {S. G. Barwick and Alice M. W. Hui and Wen-Ai Jackson},
  journal= {arXiv preprint arXiv:1906.03985},
  year   = {2019}
}

Characterising elliptic solids of $Q(4,q)$, $q$ even

Abstract

Keywords

Cite

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