Unitals of PG(2,q2) Containing Conics |
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| Authors: | Nicola Durante Alessandro Siciliano |
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| Institution: | 1. Universitá di Napoli “Federico II”, Dipartimento di Matematica ed Applicazioni, "R: Caccioppoli", Complesso Monte S.Angelo, , 80126 Napoli, Italy;2. Universitá degli Studi della Basilicata, Dipartimento di Matematica ed Informatica, , 85100 Potenza, Italy |
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| Abstract: | A unital in PG(2, q2) is a set  of  points such that each line meets  in 1 or  points. The well‐known example is the classical unital consisting of all absolute points of a unitary polarity of PG(2, q2). Unitals other than the classical one also exist in PG(2, q2) for every  . Actually, all known unitals are of Buekenhout–Metz type see F. Buekenhout, Geom Dedicata 5 (1976), 189–194, R. Metz, Geom Dedicata 8 (1979), 125–126.], and they can be obtained by a construction due to F. Buekenhout, (Geom Dedicata 5 (1976), 189–194).. The unitals constructed by R. D. Baker and G. L. Ebert (J Combin Theory Ser A 60 (1992), 67–84), and independently by J. W. P. Hirschfeld and T. Sz?nyi (Discrete Math 97 (1991), 229–242), are the union of q conics. Our Theorem 1.1 shows that this geometric property characterizes the Baker–Ebert–Hirschfeld–Sz?nyi unitals. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 101–111, 2013 |
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| Keywords: | unitals conics Veronese surface |
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