Notes on Cooperstein Ovoids in Finite Geometries of Type 𝖤6,1

Autor:	Hendrik Van Maldeghem
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	blocking set exceptional geometry maximal cocliques ovoids Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 23, p 3720 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12233720
Popis:	A Cooperstein ovoid is a set of q8+q4+1 pairwise non-collinear points in the Lie incidence geometry E6,1(q). They were introduced by Cooperstein twenty-six years ago, motivated by the fact that possible non-existence of them would imply non-existence of ovoids in hyperbolic quadrics of rank 5. Since then, no progress has been made on their existence question. We prove that Cooperstein ovoids do not exist under some natural additional conditions. In particular, Cooperstein ovoids intersecting every symplecton of E6,1(q) do not exist, Cooperstein ovoids which are the fixed points of a collineation do not exist, and Cooperstein ovoids which are the absolute points of a polarity of E6,1(q) do not exist.
Databáze:	Directory of Open Access Journals
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