## Tsukuba Journal of Mathematics

### On double coverings of a pointed non-singular curve with any Weierstrass semigroup

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 31, Number 1 (2007), 205-215.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165122

Digital Object Identifier
doi:10.21099/tkbjm/1496165122

Mathematical Reviews number (MathSciNet)
MR2337127

Zentralblatt MATH identifier
1154.14023

#### Citation

Komeda, Jiryo; Ohbuchi, Akira. On double coverings of a pointed non-singular curve with any Weierstrass semigroup. Tsukuba J. Math. 31 (2007), no. 1, 205--215. doi:10.21099/tkbjm/1496165122. https://projecteuclid.org/euclid.tkbjm/1496165122