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|Scopus||Web of Science®||Altmetric|
|Title:||Conics and caps|
|Citation:||Journal of Geometry, 2011; 100(1-2):15-28|
|Publisher:||Birkhauser Verlag Ag|
|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|
|Appears in Collections:||Mathematical Sciences publications|
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