Innovations in Incidence Geometry

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

Bence Csajbók, Tamás Héger, and György Kiss

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A t-semiarc is a point set 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. In fact, we give a more general result for small point sets with less uniform tangent distribution. We show that in PG(2,q) small t-semiarcs are related to certain small blocking sets and give some characterization theorems for small semiarcs with large collinear subsets.

Article information

Innov. Incidence Geom., Volume 14, Number 1 (2015), 1-26.

Received: 19 July 2013
Accepted: 6 October 2014
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx] 51E21: Blocking sets, ovals, k-arcs

finite plane semiarc semioval blocking set Szőnyi–Weiner Lemma


Csajbók, Bence; Héger, Tamás; Kiss, György. Semiarcs with a long secant in PG(2,q). Innov. Incidence Geom. 14 (2015), no. 1, 1--26. doi:10.2140/iig.2015.14.1.

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