Arcs in \(\mathrm{PG}(n,q)\) fixed by \(A_5\) and \(A_6\)
A \(k\)-arc in a projective space is a set of \(k\) points, no three of which are collinear. The author determines the \(k\) arcs in \(\mathrm{PG}(n,q)\) which are fixed by primitive groups isomorphic to \(A_5\) or \(A_6\). The best known examples are \(q+1\) arcs: in general these are normal rational curves and are conics in \(\mathrm{PG}(2,q)\) and twisted cubics in \(\mathrm{PG}(3,q)\). The other cases turn out to be 6-arcs or 10-arcs.
scientific article; zbMATH DE number 872720
scientific article