English

On $m$-ovoids of $Q^+(7,q)$ with $q$ odd

Combinatorics 2024-03-04 v2

Abstract

In this paper, we provide a construction of (q+1)(q+1)-ovoids of the hyperbolic quadric Q+(7,q)Q^+(7,q), qq an odd prime power, by glueing (q+1)/2(q+1)/2-ovoids of the elliptic quadric Q(5,q)Q^-(5,q). This is possible by controlling some intersection properties of (putative) mm-ovoids of elliptic quadrics. It yields eventually (q+1)(q+1)-ovoids of Q+(7,q)Q^+(7,q) not coming from a 11-system. Secondly, we also construct mm-ovoids for m{2,4,6,8,10}m \in \{ 2,4,6,8,10\} in Q+(7,3)Q^+(7,3). Therefore we first investigate how to construct spreads of \pg(3,q)\pg(3,q) that have as many secants to an elliptic quadric as possible.

Keywords

Cite

@article{arxiv.2307.03542,
  title  = {On $m$-ovoids of $Q^+(7,q)$ with $q$ odd},
  author = {Sam Adriaensen and Jan De Beule and Giovanni Giuseppe Grimaldi and Jonathan Mannaert},
  journal= {arXiv preprint arXiv:2307.03542},
  year   = {2024}
}