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Generators for cubic surfaces with two skew lines over finite fields
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Cooley, Jenny (2013) Generators for cubic surfaces with two skew lines over finite fields. Archiv der Mathematik, Volume 100 (Number 5). pp. 401-411. doi:10.1007/s00013-013-0514-3 ISSN 0003-889X.
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Official URL: http://dx.doi.org/10.1007/s00013-013-0514-3
Abstract
Let S be a smooth cubic surface defined over a field K. As observed by Segre [5] and Manin [3, 4], there is a secant and tangent process on S that generates new K-rational points from old ones. It is natural to ask for the size of a minimal generating set for S(K). In a recent paper, for fields K with at least 13 elements, Siksek [7] showed that if S contains a skew pair of K-lines, then S(K) can be generated from one point. In this paper we prove the corresponding version of this result for fields K having at least 4 elements, and slightly milder results for # K = 2 or 3.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Archiv der Mathematik | ||||
Publisher: | Birkhaeuser Verlag AG | ||||
ISSN: | 0003-889X | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 100 | ||||
Number: | Number 5 | ||||
Page Range: | pp. 401-411 | ||||
DOI: | 10.1007/s00013-013-0514-3 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access |
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