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CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES

Part of: Designs and configurations Theory of error-correcting codes and error-detecting codes Finite geometry and special incidence structures

Published online by Cambridge University Press:  29 October 2018

ANGELA AGUGLIA
ANGELA AGUGLIA*
Affiliation:
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, I-70126 Bari, Italy email angela.aguglia@poliba.it
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Abstract

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We characterize Hermitian cones among the surfaces of degree $q+1$ of $\text{PG}(3,q^{2})$ by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of $\text{PG}(4,q^{2})$ among quasi-Hermitian ones.

Keywords

Hermitian varietyquasi-Hermitian varietyalgebraic variety

MSC classification

Primary: 05B25: Finite geometries
Secondary: 51E20: Combinatorial structures in finite projective spaces 94B05: Linear codes, general
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 1 , August 2019 , pp. 1 - 8
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The author was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM).

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