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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
