Complete arcs and algebraic curves in \(\text{PG}(2,q)\)
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.
scientific article; zbMATH DE number 3983359