Complete arcs and algebraic curves in \(\text{PG}(2,q)\)
type: Item
instance of: scholarly article
title: Complete arcs and algebraic curves in \(\text{PG}(2,q)\)
zbMATH Open document ID: 0608.14016
DOI: 10.1016/0021-8693(87)90007-X
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: A \(k\)-arc of \(\text{PG}(2,q)\) is a set of \(k\) points no three of which are collinear; it is called complete if it is not contained in a \((k+1)\)-arc. B. Segre considered the question on finding the smallest bound \(k_ 0(q)\) such that any \(k\)-arc, \(k>k_ 0(q)\), is incomplete. He found bounds using the result of Hasse-Weil. The paper under review proves these results using only projective and algebraic geometry.
reviewed by: David Goss
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 3983359
zbMATH Keywords: complete k-arc
author: Joseph A. Thas
MaRDI profile type: Publication
cites work: Q3717726
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cites work: Unital intersections in finite projective planes
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cites work: Elementary proofs of two fundamental theorems of B. Segre without using the Hasse-Weil theorem
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description: scientific article; zbMATH DE number 3983359