Brill--Noether theory of smooth curves in the plane and on Hirzebruch
surfaces
Brill--Noether theory of smooth curves in the plane and on Hirzebruch
surfaces
In this paper, we describe the Brill--Noether theory of a general smooth plane curve and a general curve $C$ on a Hirzebruch surface of fixed class. It is natural to study the line bundles on such curves according to the splitting type of their pushforward along projection maps $C \to …