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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Strambach, Karl

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Joswig, Michael / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Penttila, Tim / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Sommese, Andrew J. / Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Blocking semiovals containing conics

1Dover Networks LLC, 445 Poplar Leaf Dr., Edgewater, MD 21037, USA

2Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401-5300, USA

3Department of Mathematics, Regent University, 1000 Regent University Dr., Virginia Beach, VA 23464, USA

Research supported by a sabbatical leave from the University of Mary Washington

Citation Information: . Volume 13, Issue 1, Pages 29–40, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom-2012-0025, January 2013

Publication History

Published Online:
2013-01-08

Abstract

A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). Sz˝onyi investigated an infinite family of blocking semiovals that are formed from the union of conics contained in a particular type of algebraic pencil. In this paper, the authors look at the general problem of blocking semiovals containing conics, proving a lower bound on the size of such sets and providing several new constructions of blocking semiovals containing conics. In addition, the authors investigate the natural generalization of Sz˝onyi’s construction to other conic pencils.

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