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Collineation groups of the intersection of two classical unitals

✍ Scribed by L. Giuzzi

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 149 KB
Volume: 9
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.1023

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✦ Synopsis

Abstract

Kestenband proved in [12] that there are only seven pairwise non‐isomorphic Hermitian intersections in the desarguesian projective plane PG(2, q) of square order q. 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, q) and might have different collineation groups. The projective classification of Hermitian intersections in PG(2, q) 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. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 445–459, 2001

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