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.
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