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Type: Journal article
Title: Conics and caps
Author: Barwick, S.
Jackson, W.
Quinn, C.
Citation: Journal of Geometry, 2011; 100(1-2):15-28
Publisher: Birkhauser Verlag Ag
Issue Date: 2011
ISSN: 0047-2468
Statement of
S. G. Barwick, Wen-Ai Jackson and Catherine T. Quinn
Abstract: In this article, we begin with arcs in PG(2, qⁿ ) and show that they correspond to caps in PG(2n, q) via the André/Bruck–Bose representation of PG(2, qⁿ ) in PG(2n, q). In particular, we show that a conic of PG(2, qⁿ ) that meets ℓ∞ in x points corresponds to a (qⁿ + 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.
Rights: © 2011 Springer Basel AG
RMID: 0020114871
DOI: 10.1007/s00022-011-0077-z
Appears in Collections:Mathematical Sciences publications

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