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On Perez del Pozo’s lower bound of Weierstrass weight. (English) Zbl 1403.14066
Let $$C$$ be a smooth projective curve over the complex number field with genus at least 2 and $$\sigma$$ an automorphism on $$C$$ such that the curve $$C/<\sigma>$$ has genus 0. In [Arch. Math. 86, No. 1, 50–55 (2006; Zbl 1093.14045)] A. L. Perez del Pozo obtained a lower bound, $$w$$, of the Weierstrass weights of fixed points of $$\sigma$$.In the present paper the authors find necessary and sufficient conditiomns for when this lower bound $$w$$ occurs.More precisely, they show that if the number of fixed points is at least 3 and $$P$$ is a fixed point of $$\sigma$$ with Weierstrass weight $$w(P) = w$$, the lower bound, then for the cyclic covering $$\pi$$ : $$C$$$$\rightarrow$$ $$C/<\sigma>$$ all the ramification points are total ramifications. Furthermore, they give an algorithm to compute the gap sequences of the ramification points of $$\pi$$. In addition, for the case of a unique fixed point, they give a classification of those curves $$C$$ where the Weierstrass weight of the unique fixed point is 1, 2 or 3. [K. Yoshida, Tsukuba J. Math. 17, No. 1, 221–249 (1993; Zbl 0790.30030)].
##### MSC:
 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H37 Automorphisms of curves
##### Citations:
Zbl 1093.14045; Zbl 0790.30030
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