A note on Weierstrass points of bielliptic curves
type: Item
instance of: scholarly article
title: A note on Weierstrass points of bielliptic curves
zbMATH Open document ID: 0915.14020
DOI: 10.1007/BF02678013
author: Ji-Hun Park
published in: Manuscripta Mathematica
publication date: 1999-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156358
review text: A bielliptic curve \(X\) is a two sheeted cover \(\pi:X \rightarrow E\) of an elliptic curve \(E\). The author investigates such curves for genus \(g \geq 6\). Using results of \textit{J. Komeda} [J. Reine Angew. Math. 341, 68-86 (1983; Zbl 0498.30053)], the author characterizes the \(2g-2\) ramification points of \(\pi\) as Weierstrass points with only two possible non gap sequences (H) and (L). In the main result he shows that for any preassigned number \(s\), \(0 \leq s\leq 2g-2\), \(s \neq 2\), \(2g-3\), a bielliptic curve \(X\) with \(s\) Weierstrass points of type (H) and \(2g-2-s\) points of type (L) exists.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1135223
zbMATH Keywords: Weierstrass points
zbMATH Keywords: bielliptic curves
zbMATH Keywords: ramification points
reviewed by: Manfred Streit
MaRDI profile type: Publication
cites work: Q3931657
cites work: Weights of Weierstrass points in double coverings of curves of genus one or two
cites work: Non-hyperelliptic Weierstrass points of maximal weight
cites work: On Weierstrass points whose first non-gaps are four.
cites work: Weierstrass points and double coverings of curves. With application: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups
OpenAlex ID: W2017459930
description: scientific article; zbMATH DE number 1135223