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Publication Date:
12 08 2011
ISSN:
1615-7168
DOI:
10.1515/advgeom.2011.022

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Managing Editor: Grundhöfer, Theo / Strambach, Karl

null Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / 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 / Rosehr, Nils / Bannai, Eiichi

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On the mutual position of two irreducible conics in PG(2, q), q odd

1Dipartimento di Matematica, Politecnico di Bari, Via Orbona 4, 70125 Bari, Italy

2Department of Mathematics, University of Regina, Regina, Canada S4D 0A2

3Dipartimento di Matematica e Informatica, Università della Basilicata, Campus Macchia Romana, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy

Citation Information: Advances in Geometry. Volume 11, Issue 4, Pages 603–614, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2011.022, August 2011

Publication History:

Received: 08/07/2009;
Published Online: 17/04/2012

Abstract

Given an irreducible conic in PG(2, q) with q odd, how many points of another irreducible conic 𝒟 in PG(2, q) are external to ? It is not hard to find 𝒟 such that either all its points off are external to , or none of its points are. Apart from these cases, we prove that for q large enough, the number we seek differs from by at most .

Key words.: Projective planes; conics; arcs; plane curves

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