{
  "id": "2305.06285",
  "version": "v1",
  "published": "2023-05-10T16:21:06.000Z",
  "updated": "2023-05-10T16:21:06.000Z",
  "title": "Some non-existence results on $m$-ovoids in classical polar spaces",
  "authors": [
    "Jan De Beule",
    "Jonathan Mannaert",
    "Valentino Smaldore"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we develop non-existence results for $m$-ovoids in the classical polar spaces $Q^-(2r+1,q), W(2r-1,q)$ and $H(2r,q^2)$ for $r>2$. In [4] a lower bound on $m$ for the existence of $m$-ovoids of $H(4,q^2)$ is found by using the connection between $m$-ovoids, two-character sets, and strongly regular graphs. This approach is generalized in [3] for the polar spaces $Q^-(2r+1,q), W(2r-1,q)$ and $H(2r,q^2)$, $r>2$. In [1] an improvement for the particular case $H(4,q^2)$ is obtained by exploiting the algebraic structure of the collinearity graph, and using the characterization of an $m$-ovoid as an intruiging set. In this paper, we use an approach based on geometrical and combinatorial arguments, inspired by the results from [10], to improve the bounds from [3].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T16:21:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical polar spaces",
      "non-existence results",
      "combinatorial arguments",
      "lower bound",
      "strongly regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}