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On Plane Arcs Contained in Cubic Curves

✍ Scribed by Massimo Giulietti

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
316 KB
Volume
8
Category
Article
ISSN
1071-5797

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✦ Synopsis

If the group H of the F O -rational points of a non-singular cubic curve has even order, then the coset of a subgroup of H of index two is an arc in the Galois plane of order q. The completeness of such an arc has been proved, except for the case j"0, where j is the j-invariant of the underlying cubic curve. The aim of this paper is to settle the completeness problem for the exceptional case and to provide an alternative proof of the known results.

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## Abstract The sporadic complete 12‐arc in PG(2, 13) contains eight points from a conic. In PG(2,__q__) with __q__>13 odd, all known complete __k__‐arcs sharing exactly Β½(__q__+3) points with a conic π’ž have size at most Β½(__q__+3)+2, with only two exceptions, both due to Pellegrino, which are comp