Journal of Geometry

, 100:15 | Cite as

Conics and caps

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


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.


Partial Derivative Singular Point Curve Versus Primitive Element Conic Versus 
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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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