In this paper we prove the existence of a complete cap of 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 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 PG(4n+1,q) is essentially sharp.
Small complete caps in PG(4n+1,q) / Cossidente, Antonio; Csajbok, Bence; Marino, Giuseppe; Pavese, Francesco. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - 55:1(2023), pp. 522-535. [10.1112/blms.12743]
Small complete caps in PG(4n+1,q)
Csajbok, Bence;Pavese, Francesco
2023-01-01
Abstract
In this paper we prove the existence of a complete cap of 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 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 PG(4n+1,q) is essentially sharp.File in questo prodotto:
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