Ramification points of double coverings of curves and Weierstrass points
type: Item
instance of: scholarly article
title: Ramification points of double coverings of curves and Weierstrass points
zbMATH Open document ID: 0977.14016
DOI: 10.1007/BF02505914
author: E. Ballico
author: A. Del Centina
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2000-09-20T00:00:00Z
review text: Let \(\pi: X \rightarrow C\) be a double covering with \(X\) a smooth curve and \(C\) an elliptic curve. It is known that every point in the ramification locus of \(\pi\) is a Weierstrass point of \(X\). In this paper the authors study not just the gap sequence of a single Weierstrass point of \(X\) [see \textit{J. Park}, Manuscr. Math. 95, 33-45 (1998; Zbl 0915.14020)], but the gap sequence of all points of the ramification locus of \(\pi\). In particular, following \textit{E. Ballico} and \textit{S. J. Kim} [Indag. Math., New Ser. 9, No. 2, 155-159 (1998; Zbl 0930.14023)], they prove the existence of bielliptic curves with a certain number of suitable ramification Weierstrass points and a non-ramification Weierstrass point with prescribed sequence of non-gaps. They also study the problem for triple cyclic coverings of elliptic curves.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 1472055
zbMATH Keywords: Weierstrass points
zbMATH Keywords: bielliptic curves
zbMATH Keywords: gap-sequences
zbMATH Keywords: triple cyclic coverings
reviewed by: Caterina Cumino
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472055