Commuting polarities and maximal partial ovoids of H(4,q2) |
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Authors: | Antonio Cossidente Alessandro Siciliano |
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Institution: | Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Contrada Macchia Romana, 85100 Potenza, Italy |
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Abstract: | In PG(4,q2), q odd, let Q(4,q2) be a non‐singular quadric commuting with a non‐singular Hermitian variety H(4,q2). Then these varieties intersect in the set of points covered by the extended generators of a non‐singular quadric Q0 in a Baer subgeometry Σ0 of PG(4,q2). It is proved that any maximal partial ovoid of H(4,q2) intersecting Q0 in an ovoid has size at least 2(q2+1). Further, given an ovoid O of Q0, we construct maximal partial ovoids of H(4,q2) of size q3+1 whose set of points lies on the hyperbolic lines 〈P,X〉 where P is a fixed point of O and X varies in O\{P}. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 307–313, 2009 |
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Keywords: | commuting polarities Hermitian varieties ovoids |
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