Ryo Kawaguchi (Osaka Univ.)

Title : The gonality of a curve on a toric surface

Abstract :

The gonality is one of significant invariants in the study of algebraic curves. Although it is often difficult to determine it for a given curve, M. Namba ('84) showed that gon(C)=d-1 if C is a nonsingular plane curve of degree d. Besides, the gonality of a curve on a Hirzebruch surface was computed by G. Martens ('96). In this talk, we consider more general surfaces called "toric surfaces", and determine the gonality of curves on them. Furthermore, we can see the Clifford dimension of such curves and the set of gonality morphisms (i.e. the morphisms whose degree are equal to the gonality).

For the proof, we will utilize the close relation between toric varieties and the geometry of convex polytopes.