Conics and caps

被引：3
|
作者：
Barwick S.G. [1 ]
Jackson W.-A. [1 ]
Quinn C.T. [1 ]
机构：
[1] School of Mathematical Sciences, University of Adelaide
来源：
Journal of Geometry | 2011年 / 100卷 / 1-2期
关键词：
Partial Derivative; Singular Point; Curve Versus; Primitive Element; Conic Versus;
D O I：
10.1007/s00022-011-0077-z
中图分类号：
学科分类号：
摘要：
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. © 2011 Springer Basel AG.
引用
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页码：15 / 28
页数：13
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