Small complete caps in ${\rm PG}(4n + 1, q)$

Antonio Cossidente; Bence Csajbók; Giuseppe Marino; Francesco Pavese

Small complete caps in ${\rm PG}(4n + 1, q)$

Combinatorics 2021-06-01 v1

Authors: Antonio Cossidente , Bence Csajbók , Giuseppe Marino , Francesco Pavese

Abstract

In this paper we prove the existence of a complete cap of ${\rm PG}(4n+1, q)$ of size $2(q^{2n+1}-1)/(q-1)$ , for each prime power $q>2$ . It is obtained by projecting two disjoint Veronese varieties of ${\rm PG}(2n^2+3n, q)$ from a suitable $(2n^2-n-2)$ -dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of ${\rm PG}(4n+1, q)$ is essentially sharp.

Keywords

linear sets

Cite

@article{arxiv.2105.14939,
  title  = {Small complete caps in ${\rm PG}(4n + 1, q)$},
  author = {Antonio Cossidente and Bence Csajbók and Giuseppe Marino and Francesco Pavese},
  journal= {arXiv preprint arXiv:2105.14939},
  year   = {2021}
}

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