Adelaide Research & Scholarship
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https://hdl.handle.net/2440/69160
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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 1420-8997 |
| Statement of Responsibility: | 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 |
| DOI: | 10.1007/s00022-011-0077-z |
| Published version: | http://dx.doi.org/10.1007/s00022-011-0077-z |
| Appears in Collections: | Aurora harvest 5 Mathematical Sciences publications |
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