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- W4364380312 abstract "An m $m$ -ovoid of a finite polar space P $mathcal {P}$ is a set O $mathcal {O}$ of points such that every maximal subspace of P $mathcal {P}$ contains exactly m $m$ points of O $mathcal {O}$ . In the case when P $mathcal {P}$ is an elliptic quadric Q − ( 2 r + 1 , q ) $mathcal {Q}^-(2r+1, q)$ of rank r $r$ in F q 2 r + 2 $mathbb {F}_q^{2r+2}$ , we prove that an m $m$ -ovoid exists only if m $m$ satisfies a certain modular equality, which depends on q $q$ and r $r$ . This condition rules out many of the possible values of m $m$ . Previously, only a lower bound on m $m$ was known, which we slightly improve as a byproduct of our method. We also obtain a characterization of the m $m$ -ovoids of Q − ( 7 , q ) $mathcal {Q}^{-}(7,q)$ for q = 2 $q = 2$ and ( m , q ) = ( 4 , 3 ) $(m, q) = (4, 3)$ ." @default.
- W4364380312 created "2023-04-12" @default.
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- W4364380312 date "2023-04-11" @default.
- W4364380312 modified "2023-09-30" @default.
- W4364380312 title "A modular equality for m$m$‐ovoids of elliptic quadrics" @default.
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- W4364380312 doi "https://doi.org/10.1112/blms.12830" @default.
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