A characterization of the tangent lines to a Hermitian curve
A characterization of the tangent lines to a Hermitian curve
In the projective Desarguesian plane \(PG(2,q^ 2)\) let H be a Hermitian curve (i.e. the locus of the absolute points of a unitary polarity). This paper is concerned with properties of Hermitian curves of \(PG(2,q^ 2)\) with \(q\geq 3\). The main result reads as follows. If \(F=\{x_ 1,x_ 2,...,x_ q\}\) is a set of \(q^ 2\) points of \(PG(2,q^ 2)\backslash H\) such that each line \(x_ ix_ j\), \(i\neq j\), is a tangent to H, then the points of F all belong to the same tangent to H.
- University of Perugia Italy
absolute points, Combinatorial structures in finite projective spaces, Combinatorial aspects of finite geometries, unitary polarity, Baer subplane, Hermitian curve projective Desarguesian plane
absolute points, Combinatorial structures in finite projective spaces, Combinatorial aspects of finite geometries, unitary polarity, Baer subplane, Hermitian curve projective Desarguesian plane
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