Open Access
2015 Semiarcs with a long secant in PG(2,q)
Bence Csajbók, Tamás Héger, György Kiss
Innov. Incidence Geom. 14: 1-26 (2015). DOI: 10.2140/iig.2015.14.1


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.


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Bence Csajbók. Tamás Héger. György Kiss. "Semiarcs with a long secant in PG(2,q)." Innov. Incidence Geom. 14 1 - 26, 2015.


Received: 19 July 2013; Accepted: 6 October 2014; Published: 2015
First available in Project Euclid: 28 February 2019

zbMATH: 1351.51007
MathSciNet: MR3450949
Digital Object Identifier: 10.2140/iig.2015.14.1

Primary: 51E20 , 51E21

Keywords: blocking set , finite plane , semiarc , semioval , Szőnyi–Weiner Lemma

Rights: Copyright © 2015 Mathematical Sciences Publishers

Vol.14 • 2015
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