Innovations in Incidence Geometry

Projections of quadrics in finite projective spaces of odd characteristic

Frank De Clerck and Nikias De Feyter

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Abstract

The set of points obtained by projecting a quadric from a point off the quadric on a hyperplane has many interesting properties. Hirschfeld and Thas provided a characterization of this set, only by means of its intersection pattern with lines. However, their result only holds when the finite field has even order. Here, we extend their result to finite fields of odd order.

Article information

Source
Innov. Incidence Geom., Volume 3, Number 1 (2006), 51-80.

Dates
Received: 31 August 2005
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323240

Digital Object Identifier
doi:10.2140/iig.2006.3.51

Mathematical Reviews number (MathSciNet)
MR2267606

Zentralblatt MATH identifier
1113.51001

Subjects
Primary: 05B25: Finite geometries [See also 51D20, 51Exx] 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

Keywords
projections of quadrics sets of points in projective space with prescribed intersection types internal points of a conic external points of a conic

Citation

De Clerck, Frank; De Feyter, Nikias. Projections of quadrics in finite projective spaces of odd characteristic. Innov. Incidence Geom. 3 (2006), no. 1, 51--80. doi:10.2140/iig.2006.3.51. https://projecteuclid.org/euclid.iig/1551323240


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