Weierstrass gap sequences on curves on toric surfaces

Abstract

In this paper, we consider a nonsingular curve C on a nonsingular compact toric surface S and intersection points of C and T-invariant divisors on S. We provide a sufficient condition for a positive integer to be a gap value of C at such points. Under a suitable assumption, it becomes the necessary and sufficient condition. We determine several Weierstrass gap sequences at infinitely near points of a point on a plane curve by using this method.