An m-ovoid of a finite polar space P is a set O of points such that every maximal subspace of P contains exactly m points of O. In the case when P is an elliptic quadric Q(-)(2r+ 1, q) of rank r in F-q(2r+2), we prove that an m-ovoid exists only if m satisfies a certain modular equality, which depends on q and r. This condition rules out many of the possible values of r. Previously, only a lower bound on m was known, which we slightly improve as a byproduct of our method. We also obtain a characterization of them-ovoids of Q(-)(7, q) for q = 2 and (m, q) = (4, 3).

A modular equality for m-ovoids of elliptic quadrics / Gavrilyuk, Al; Metsch, K; Pavese, F. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 55:4(2023), pp. 1957-1970. [10.1112/blms.12830]

A modular equality for m-ovoids of elliptic quadrics

Pavese, F
2023-01-01

Abstract

An m-ovoid of a finite polar space P is a set O of points such that every maximal subspace of P contains exactly m points of O. In the case when P is an elliptic quadric Q(-)(2r+ 1, q) of rank r in F-q(2r+2), we prove that an m-ovoid exists only if m satisfies a certain modular equality, which depends on q and r. This condition rules out many of the possible values of r. Previously, only a lower bound on m was known, which we slightly improve as a byproduct of our method. We also obtain a characterization of them-ovoids of Q(-)(7, q) for q = 2 and (m, q) = (4, 3).
2023
A modular equality for m-ovoids of elliptic quadrics / Gavrilyuk, Al; Metsch, K; Pavese, F. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 55:4(2023), pp. 1957-1970. [10.1112/blms.12830]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/262543
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