Journal article

Publication year: 2023

Pages: 1957-1970

Journal: Bulletin of the London Mathematical Society

Volume number: 55

Issue number: 4

ISSN: 0024-6093

eISSN: 1469-2120

DOI Link: https://doi.org/10.1112/blms.12830

Publisher: Wiley

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).

Harvard Citation style: Gavrilyuk, A., Metsch, K. and Pavese, F. (2023) A modular equality for m-ovoids of elliptic quadrics, Bulletin of the London Mathematical Society, 55(4), pp. 1957-1970. https://doi.org/10.1112/blms.12830

APA Citation style: Gavrilyuk, A., Metsch, K., & Pavese, F. (2023). A modular equality for m-ovoids of elliptic quadrics. Bulletin of the London Mathematical Society. 55(4), 1957-1970. https://doi.org/10.1112/blms.12830