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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 18, Issue 2

Issues

Feet in orthogonal-Buekenhout–Metz unitals

N. Abarzúa / R. Pomareda / O. Vega
Published Online: 2018-03-26 | DOI: https://doi.org/10.1515/advgeom-2017-0050

Abstract

Given an orthogonal-Buekenhout–Metz unital Uα,β, embedded in PG(2, q2), and a point PUα,β, we study the set τP(Uα,β) of feet of P in Uα,β. We characterize geometrically each of these sets as either q + 1 collinear points or as q + 1 points partitioned into two arcs. Other results about the geometry of these sets are also given.

Keywords: Unitals; projective planes

MSC 2010: Primary 51; 05; Secondary 20

References

  • [1]

    A. Aguglia, G. L. Ebert, A combinatorial characterization of classical unitals. Arch. Math. (Basel) 78 (2002), 166–172. MR1888419 Zbl 1006.51004CrossrefGoogle Scholar

  • [2]

    R. D. Baker, G. L. Ebert, Intersection of unitals in the Desarguesian plane. In: Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989), volume 70, 87–94, 1990. MR1041587 Zbl 0695.51009Google Scholar

  • [3]

    S. Barwick, G. Ebert, Unitals in projective planes. Springer 2008. MR2440325 Zbl 1156.51006Google Scholar

  • [4]

    F. Buekenhout, Existence of unitals in finite translation planes of order q2 with a kernel of order q. Geometriae Dedicata 5 (1976), 189–194. MR0448236 Zbl 0336.50014Google Scholar

  • [5]

    P. Dembowski, Finite geometries. Springer 1997. MR1434062 Zbl 0865.51004Google Scholar

  • [6]

    N. Durante, A. Siciliano, Unitals of PG(2, q2) containing conics. J. Combin. Des. 21 (2013), 101–111. MR3011984 Zbl 1273.05025Google Scholar

  • [7]

    J. W. P. Hirschfeld, Projective geometries over finite fields. Oxford Univ. Press 1998. MR1612570 Zbl 0899.51002Google Scholar

  • [8]

    J. W. P. Hirschfeld, T. Szőnyi, Sets in a finite plane with few intersection numbers and a distinguished point. Discrete Math. 97 (1991), 229–242. MR1140805 Zbl 0748.51011CrossrefGoogle Scholar

  • [9]

    V. Krčadinac, K. Smoljak, Pedal sets of unitals in projective planes of order 9 and 16. Sarajevo J. Math. 7(20) (2011), 255–264. MR2906536 Zbl 1277.51010Google Scholar

  • [10]

    J. A. Thas, A combinatorial characterization of Hermitian curves. J. Algebraic Combin. 1 (1992), 97–102. MR1162643 Zbl 0784.51023CrossrefGoogle Scholar

About the article


Received: 2016-04-21

Published Online: 2018-03-26

Published in Print: 2018-04-25


Funding: During the time this project was done, the second author was funded by Fondecyt project # 1140510.


Citation Information: Advances in Geometry, Volume 18, Issue 2, Pages 229–236, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0050.

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