A characterization of the family of secant lines to a hyperbolic quadric in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si4.svg"><mml:mrow><mml:mtext>PG</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e39" altimg="si5.svg"><mml:mi>q</mml:mi></mml:math> odd

Pradhan, Puspendu; Sahu, Bikramaditya

doi:10.1016/j.disc.2020.112044

Cited by 6 publications

(3 citation statements)

References 7 publications

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“…The authors of [13] studied line sets in PG(3, q) that satisfy a list of axioms. Their main theorem states that for q ≥ 7 each such line set is either the set of secant lines with respect to a hyperbolic quadric or belongs to a hypothetical family of line sets.…”

Section: Introductionmentioning

confidence: 99%

“…Their main theorem states that for q ≥ 7 each such line set is either the set of secant lines with respect to a hyperbolic quadric or belongs to a hypothetical family of line sets. The question whether this hypothetical family of line sets is nonempty was left open in [13]. Further investigations showed that these line sets are related to quadratic sets of the Klein quadric, see [10].…”

Section: Introductionmentioning

confidence: 99%

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Pseudo-embeddings and quadratic sets of quadrics

Bruyn

Gao

2021

Des. Codes Cryptogr.

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A quadratic set of a nonsingular quadric Q of Witt index at least three is defined as a set of points intersecting each subspace of Q in a possibly reducible quadric of that subspace. By using the theory of pseudo-embeddings and pseudohyperplanes, we show that if Q is one of the quadrics Q + (5, 2), Q(6, 2), Q − (7, 2), then the quadratic sets of Q are precisely the intersections of Q with the quadrics of the ambient projective space of Q. In order to achieve this goal, we will determine the universal pseudo-embedding of the geometry of the points and planes of Q.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pseudo-embeddings and quadratic sets of quadrics

Bruyn

Gao

2021

Des. Codes Cryptogr.

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“…A characterization of the family of external lines to a hyperbolic quadric in PG(3, q) was given in [4] for all q (also see [6] for a different characterization in terms of a point-subset of the Klein quadric in PG (5, q)). In a recent paper [8], a characterization of secant lines to a hyperbolic quadric is given for all odd q, q ≥ 7. In this paper, we give a characterization of the family of planes meeting a hyperbolic quadric in PG (3, q) in an irreducible conic.…”

Section: Introductionmentioning

confidence: 99%