Base point free pencils of small degree on certain smooth curves

Abstract

We give sufficient conditions on numbers d and m such that a linear system of degree m on the normalization C of a plane curve \(\overline {C}\) of degree d which is in a certain sense not too singular is in the natural way induced by either a pencil of lines or a pencil of conics in the plane. Those results generalize results on nodal and cuspidal plane curves and seem to complement the recent results of [2]. We present a new approach via the geometry of curves in \({\Bbb P}_1\times {\Bbb P}_2\).