On planar arcs of size $(q+3)/2$
Abstract
The subject of this paper is the study of small complete arcs in $\mathrm{PG}(2,q)$, for $q$ odd, with at least $(q+1)/2$ points on a conic. We give a short comprehensive proof of the completeness problem left open by Segre in his seminal work [20]. This gives an alternative to Pellegrino's long proof which was obtained in a series of papers in the 1980s. As a corollary of our analysis, we obtain a counterexample to a misconception in the literature [6].
- Publication:
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arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.10994
- arXiv:
- arXiv:2105.10994
- Bibcode:
- 2021arXiv210510994G
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Algebraic Geometry