Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes (Q1377781)

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scientific article; zbMATH DE number 1110041
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Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes
scientific article; zbMATH DE number 1110041

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    Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes (English)
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    19 January 1999
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    This is a survey (without proofs) on the interrelation of the objects in the title of the paper. It contains the following information: connection between inversive planes and ovoids in \(\text{PG}(3, q)\); some important characterizations of classical inversive planes; projective and inversive planes of small order: uniqueness and existence; all known ovoids of \(\text{PG}(3,q)\) and of the quadric (generalized quadrangle) \(\text{Q}(4,q)\); existence and uniqueness of ovoids of the quadric \(\text{Q}(2n,q)\). Finally, there is a very interesting appendix on the equivalence of flocks of cones giving rise to translation generalized quadrangles, and a certain type of ovoids of \(\text{Q}(4,q)\) (and this is a new result, with an entirely geometric proof).
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    spread
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    translation plane
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    survey
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    inversive planes
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    ovoids
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    existence
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    uniqueness
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    generalized quadrangles
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