Kestenband proved in \cite{K1} that there are only seven pairwise non-isomorphic Hermitian intersections in the desarguesian projective plane $\PG(2,\qq)$ of square order $\qq$. His classification is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be projectively equivalent in $\PG(2,\qq)$ and might have different collineation groups. The projective classification of Hermitian intersections in $\PG(2,\qq)$ is the main goal in this paper. It turns out that each of Kestenband's classes consists of projectively equivalent Hermitian intersections. A complete classification of the linear collineation groups preserving a Hermitian intersection is also given.

Collineation groups of the intersection of two classical unitals

GIUZZI, Luca
2001-01-01

Abstract

Kestenband proved in \cite{K1} that there are only seven pairwise non-isomorphic Hermitian intersections in the desarguesian projective plane $\PG(2,\qq)$ of square order $\qq$. His classification is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be projectively equivalent in $\PG(2,\qq)$ and might have different collineation groups. The projective classification of Hermitian intersections in $\PG(2,\qq)$ is the main goal in this paper. It turns out that each of Kestenband's classes consists of projectively equivalent Hermitian intersections. A complete classification of the linear collineation groups preserving a Hermitian intersection is also given.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/24707
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