Collineation Groups of the Intersection of Two Classical Unitals

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 classi®cation 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 classi®cation 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 classi®cation of the linear collineation groups preserving a Hermitian intersection is also given. # 2001 John Wiley & Sons, Inc. J Combin Designs 9: 445±459, 2001