On the sharpness of a theorem of B. Segre (Q1084336)
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scientific article; zbMATH DE number 3977823
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sharpness of a theorem of B. Segre |
scientific article; zbMATH DE number 3977823 |
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On the sharpness of a theorem of B. Segre (English)
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1986
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Starting with the cyclic partition of \(\mathrm{PG}(2,q)\) (with \(q\) a square) into disjoint Baer-subplanes a complete \(q-\sqrt{q}+1\)-arc of \(\mathrm{PG}(2,q)\) is constructed, and so the sharpness of an estimation of \textit{B. Segre} [Atti. Accad. Naz. Linzei, Mem., Cl. Sci. Fis. Mat. Nat., Sez. I, VIII. Ser. 8, 133--236 (1967; Zbl 0194.21503)] for the number of points on a complete arc is proved. Furthermore it is shown that these constructions' results are isomorphic to the \(q-\sqrt{q}+1\)-arcs constructed by \textit{B. C. Kestenband} [Geom. Dedicata 11, 107--117 (1981; Zbl 0452.51007)]. Therefore his arcs are proved to be complete.
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intersection of unitals
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complete arc
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