The gonality conjecture for curves on certain toric surfaces

Abstract

The gonality is one of important invariants in the study of linear systems on curves. The gonality conjecture which was posed by Green and Lazarsfeld predicts that we can read off the gonality of a curve from any one line bundle of sufficiently large degree on the curve. This conjecture had been proved for curves on Hirzebruch surfaces by Aprodu. In this artlcle, we will extend this result for curves on certain toric surfaces.