Weierstrass gap sequences at the ramification points of trigonal Riemann surfaces
type: Item
instance of: scholarly article
title: Weierstrass gap sequences at the ramification points of trigonal Riemann surfaces
zbMATH Open document ID: 0649.14009
DOI: 10.1016/0022-4049(88)90105-3
author: Takao Kato
author: Ryutaro Horiuchi
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: A trigonal Riemann surface M of genus \(g\geq 5\) is of n-th kind if \(\ell (nD)=n+1\) and \(\ell (n+1)D\geq n+3\), where D is the divisor of degree 3 associated to M. Total and ordinary ramification points of M as 3-sheeted covering of \({\mathbb{P}}^ 1\) can be classified into two types [cf. \textit{M. Coppens}, Indagationes Math. 47, 245-276 (1985; Zbl 0592.14025) and J. Pure Appl. Algebra 43, 11-25 (1986; Zbl 0616.14012)]. In this article the authors give a normalized defining equation of a trigonal Riemann surface M of n-th kind, and by investigating it they determine the types of ramification points of M and show the existence of Riemann surfaces with various types of ramification points. Some estimates on the numbers of ramification points are also obtained.
reviewed by: Ryutaro Horiuchi
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 4059564
zbMATH Keywords: Weierstrass gap sequence
zbMATH Keywords: trigonal Riemann surface of n-th kind
zbMATH Keywords: ramification points
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90105-3
OpenAlex ID: W2024054077
cites work: Q3256658
cites work: Q3720720
cites work: The Weierstrass gap sequence of the ordinary ramification points of trigonal coverings of \({\mathbb{P}}^ 1\); existence of a kind of Weierstrass gap sequence
cites work: On Weierstraß points whose first non-gaps are three.
description: scientific article; zbMATH DE number 4059564