Shult sets and translation ovoids of the Hermitian surface

A Cossidente; G. L Ebert; G Marino; A Siciliano

doi:10.1515/ADVGEOM.2006.032

Published by De Gruyter October 16, 2006

Shult sets and translation ovoids of the Hermitian surface

A Cossidente , G. L Ebert , G Marino and A Siciliano

From the journal Advances in Geometry

https://doi.org/10.1515/ADVGEOM.2006.032

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Abstract

Starting with carefully chosen sets of points in the Desarguesian affine plane AG(2; q²) and using an idea first formulated by E. Shult, several infinite families of translation ovoids of the Hermitian surface are constructed. Various connections with locally Hermitian 1-spreads of 𝒬⁻(5, q) and semifield spreads of PG(3, q) are also discussed. Finally, geometric characterization results are developed for the translation ovoids arising in the so-called classical and semiclassical settings.

Key words: Hermitian surface; translation ovoid

(Communicated by W. M. Kantor)

Received: 2005-01-18

Published Online: 2006-10-16

Published in Print: 2006-10-01

Shult sets and translation ovoids of the Hermitian surface

Abstract

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