Symplectic spreads in PG(3, q ), inversive planes and projective planes
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TLDR
Some important characterizations of finiteInversive planes, the inversive planes of small order, the planes ofSmall order arising from symplectic spreads of PG(3, q ), and all known classes of ovoids of PG and Q (4, q ).About:
This article is published in Discrete Mathematics.The article was published on 1997-09-15 and is currently open access. It has received 24 citations till now. The article focuses on the topics: Ovoid & Quadric.read more
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Translation ovoids of orthogonal polar spaces
Guglielmo Lunardon,O. Polverino +1 more
Journal ArticleDOI
Translation Ovoids of Generalized Quadrangles and Hexagnos
TL;DR: In this paper, the notion of translation ovoid in the classical generalized quadrangles and hexagons of order q was defined, and all known translation spreads are defined dually; a modification of the known ovoids in the generalized hexagon H(q), q = 32h+1, yields new ovoids of that hexagon Dualizing and projecting along reguli, and constructing an alternative construction of the Roman ovoids due to Thas and Payne also, they construct a new translation spread in h(q) for any ≡ 1 mod 3, q odd, with the
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A New Semifield Flock
TL;DR: The new semifield flock ofPG is constructed associated with the Penttila?Williams translation ovoid and the associated generalized quadrangle and its translation dual are studied.
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Flocks, Ovoids of Q(4,q)and Designs
TL;DR: In this paper, it was shown that an ovoid O of Q(4,q),q odd, is the Thas' ovoid associated with a semifield flock if and only if O represents, on the Klein quadric, a symplectic spread of PG(3,q) whose associated plane is a semifiled plane.
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On the classification of semifield flocks
TL;DR: In this article, a classical lemma of Weil is used to characterise quadratic polynomials f with coefficients GF ( q n ), q odd, with the property that f (x ) is a non-zero square for all x ∈ GF( q ), and this characterisation was used to prove the main theorem that there are no subplanes of order q contained in the set of internal points of a conic in PG (2, q n ) for q ⩾4 n 2 −8 n +2.
References
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Book
Finite projective spaces of three dimensions
TL;DR: Projective Geometrics Over Finite Fields (OUP, 1979) as mentioned in this paper considers projective spaces of three dimensions over a finite field and examines properties of four and five dimensions, fundamental applications to translation planes, simple groups, and coding theory.
BookDOI
General Galois geometries
TL;DR: In this paper, the authors define Hermitian varieties, Grassmann varieties, Veronese and Segre varieties, and embedded geometries for finite projective spaces of three dimensions.
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Generalized quadrangles and flocks of cones
TL;DR: It is proved that with a set of q upper triangular 2 × 2-matrices over GF(q) of a certain type, there corresponds a generalized quadrangle of order (q2, q) and with each flock of the quadratic cone there corresponds such a setof matrices.