Weights of Weierstrass points in double coverings of curves of genus one or two
type: Item
instance of: scholarly article
title: Weights of Weierstrass points in double coverings of curves of genus one or two
zbMATH Open document ID: 0603.14014
DOI: 10.1007/BF01186655
author: Arnaldo Garcia
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155148
review text: Let X be a compact Riemann surface of genus \(g.\) A Weierstrass point \(P\in X\) has non-zero weight w(P) which is defined by \(w(P)=g(3g+1)- \sum^{g}_{j=1}m_ j\) where \(\{m_ j\}\) is the sequence of non-gaps at P. The authors proves: if \(g\geq 11\), and X is non-hyperelliptic, then X is a double covering of a surface of genus \(1\) if and only if there exists \(P\in X\) with \(g^ 2-g>2w(P)\geq g^ 2-5g+6\); and a similar result with genus \(1\) replaced by genus \(2.\) This extends the results and uses the methods of \textit{T. Kato} [Math. Ann. 239, 141-147 (1979; Zbl 0401.30037)]. The techniques are standard in this area and use extensively the fact that the non-gaps form a semi-group. An interesting key lemma: If X is non-hyperelliptic, then for \(P\in X\), \(m_ j\geq 2j+1\) for \(1\leq j\leq g-2\), \(m_{g-1}\leq 2g-2\) and \(m_ g=2g\).
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 3973034
zbMATH Keywords: weight of Weierstrass point
zbMATH Keywords: compact Riemann surface
zbMATH Keywords: sequence of non- gaps
reviewed by: C. Maclachlan
MaRDI profile type: Publication
cites work: Q3931656
cites work: Some Remarks on Weierstrass Points
cites work: On Weierstraß points whose first non-gaps are three.
cites work: On criteria of \({\widetilde g}\)-hyperellipticity
cites work: Non-hyperelliptic Weierstrass points of maximal weight
cites work: Weierstrass Points on Compact Riemann Surfaces
OpenAlex ID: W2023413498
description: scientific article; zbMATH DE number 3973034