Let $V$ be a smooth projective curve over the complex number field with genus $g \geq 2$, and let $\sigma$ be an automorphism on $V$ such that the quotient curve $V/\langle \sigma \rangle$ has genus 0. We write $d$ (resp., $b$) for the order of $\sigma$ (resp., the number of fixed points of $\sigma$). When $d$ and $b$ are fixed, the lower bound of the (Weierstrass) weights of fixed points of $\sigma$ was obtained by Perez del Pozo . We obtain necessary and sufficient conditions for when the lower bound is attained.
"On Perez Del Pozo's lower bound of Weierstrass weight." Kodai Math. J. 41 (2) 332 - 347, June 2018. https://doi.org/10.2996/kmj/1530496845