Abstract
Let $H$ be a Weierstrass semigroup, i.e., the set $H(P)$ of integers which are pole orders at $P$ of regular functions on $C \setminus \{P\}$ for some pointed non-singular curve $(C, P)$. In this paper for any Weierstrass semi group $H$ we construct a double covering $\pi:\tilde{C} \to C$ with a ramification point $\tilde{P}$ such that $H(\pi(\tilde{P})) = H$. We also determine the semigroup $H(\tidle{P})$. Moreover, in the case where $H$ starts with 3 we investigate the relation between the semigroup $H(\tilde{P})$ and the Weierstrass semigroup of a total ramification point on a cyclic covering of the projective line with degree 6.
Citation
Jiryo Komeda. Akira Ohbuchi. "On double coverings of a pointed non-singular curve with any Weierstrass semigroup." Tsukuba J. Math. 31 (1) 205 - 215, June 2007. https://doi.org/10.21099/tkbjm/1496165122
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