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Journal of Geometry

, 100:15 | Cite as

Conics and caps

  • S. G. Barwick
  • Wen-Ai Jackson
  • Catherine T. Quinn
Article

Abstract

In this article, we begin with arcs in PG(2, q n ) and show that they correspond to caps in PG(2n, q) via the André/Bruck–Bose representation of PG(2, q n ) in PG(2n, q). In particular, we show that a conic of PG(2, q n ) that meets ℓ in x points corresponds to a (q n  + 1 − x)-cap in PG(2n, q). If x = 0, this cap is the intersection of n quadrics. If x = 1 or 2, this cap is contained in the intersection of n quadrics and we discuss ways of extending these caps. We also investigate the structure of the n quadrics.

Keywords

Partial Derivative Singular Point Curve Versus Primitive Element Conic Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • S. G. Barwick
    • 1
  • Wen-Ai Jackson
    • 1
  • Catherine T. Quinn
    • 1
  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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