Shult sets and translation ovoids of the Hermitian surface
A Cossidente, GL Ebert, G Marino, A Siciliano - 2006 - degruyter.com
A Cossidente, GL Ebert, G Marino, A Siciliano
2006•degruyter.comStarting with carefully chosen sets of points in the Desarguesian affine plane AG (2; q 2) 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.
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.
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.
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