Symmetries of arcs (Q1323831)

The authors' introduction: ``We denote by \(P \Gamma L(3,q)\) the full collineation group of \(PG(2,q)\) while \(PGL (3,q)\) denotes the group of homographies of \(PG (2,q)\). The stabiliser of a \(k\)-arc \({\mathcal K}\) in \(P \Gamma L(3,q)\) is called the collineation stabiliser of \({\mathcal K}\), while the stabiliser of \({\mathcal K}\) in \(PGL (3,q)\) is the homography stabiliser of \({\mathcal K}\). The purpose of this paper is to classify \(k\)-arcs of \(PG (2,q)\), \(q\) even, which have \(k \geq q-1\) points and a transitive homography stabiliser. Our main results are that a \((q + 1)\)-arc of \(PG (2,q)\), \(q\) even, with a transitive homography stabiliser is a conic, a \(q\)-arc of \(PG (2,q)\), \(q\) even, with a transitive homography stabiliser is a translation \(q\)-arc and a \((q-1)\)-arc of \(PG (2,q)\), \(q=2^ h\), with a transitive homography stabiliser is a monomial \((q-1)\)-arc provided \(h \not \equiv 2\) (modulo 12)''.