A characterization of Hermitian curves

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1991 English Publisher:Springer Science and Business Media LLCJournal:Journal of Geometry, volume 41, pages 72-78 (issn: 0047-2468, eissn: 1420-8997,

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Authors: Hirschfeld, J. W. P.; Storme, L.; Thas, J. A.; Voloch, J. F.;

doi: 10.1007/bf01258509

A characterization of Hermitian curves

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Abstract

Hermitian curves can be characterized in various ways. The authors present a new characterization by showing that in \(PG(2,q)^ 2\), with \(q\neq 2\), an algebraic curve of degree \(q+1\), without linear components, and with at least \(q^ 3+1\) points in \(PG(2,q^ 2)\) is a Hermitian curve. They also explain why the result does not hold for \(GF(4)\) or if linear components are allowed.

Related Organizations

University of Sussex
United Kingdom
Instituto Nacional de Matemática Pura e Aplicada
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Ghent University
Belgium

Keywords

Hermitian curve, unital, Blocking sets, ovals, \(k\)-arcs, Hermitian arc

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