On Perez Del Pozo’s lower bound of Weierstrass weight

Abstract

Let V be a smooth projective curve over the complex number field with genus g ≥ 2, and let σ be an automorphism on V such that the quotient curve V/<σ> has genus 0. We write d (resp., b) for the order of σ (resp., the number of fixed points of σ). When d and b are fixed, the lower bound of the (Weierstrass) weights of fixed points of σ was obtained by Perez del Pozo [7]. We obtain necessary and sufficient conditions for when the lower bound is attained.