2006/07/05 by Massimo Giulietti, Giulietti, Massimo
Computer Science · Engineering · Mathematics · #51E21 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:51E21
paper · pdf · doi:10.48550/arxiv.math/0607118
arxiv created 2006/07/05 · openalex publication_date 2006/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
All sets of lines providing a partition of the set of internal points to a conic C in PG(2,q), q odd, are determined. There exist only three such linesets up to projectivities, namely the set of all nontangent lines to C through an external point to C, the set of all nontangent lines to C through a point in C, and, for square q, the set of all nontangent lines to C belonging to a Baer subplane with at least 5 common points with C. This classification theorem is the analogous of a classical result by Segre and Korchmaros characterizing the pencil of lines through an internal point to C as the unique set of lines, up to projectivities, which provides a partition of the set of all noninternal points to C. However, the proof is not analogous, since it does not rely on the famous Lemma of Tangents of Segre. The main tools in the present paper are certain partitions in conics of the set of all internal points to C, together with some recent combinatorial characterizations of blocking sets of non-secant lines, and of blocking sets of external lines.