Semiarcs with a long secant in PG(2,q)

Csajbók, Bence and Héger, Tamás and Kiss, György (2015) Semiarcs with a long secant in PG(2,q). INNOVATIONS IN INCIDENCE GEOMETRY, 14 (1). pp. 1-26. ISSN 1781-6475

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Abstract

A t-semiarc is a pointset St with the property that the number of tangent lines to St at each of its points is t. We show that if a small t-semiarc St in PG(2, q) has a large collinear subset K, then the tangents to St at the points of K can be blocked by t points not in K. We also show that small t-semiarcs are related to certain small blocking sets. Some characterization theorems for small semiarcs with large collinear subsets in PG(2, q) are given.

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