The existence of \(k\)-gonal curves possessing exactly two linear systems \(g_ k^ 1\)
type: Item
instance of: scholarly article
title: The existence of \(k\)-gonal curves possessing exactly two linear systems \(g_ k^ 1\)
zbMATH Open document ID: 0870.14023
published in: Mathematische Annalen
publication date: 1997-09-17T00:00:00Z
review text: The main theorem proved in this paper is the following. For all integers \(g\) and \(k\) satisfying the inequalities \(4\leq k\leq[(g+1)/2]\) and \(8\leq g\leq(k-1)^2\) there exists a \(k\)-gonal curve of genus \(g\) possessing exactly 2 independent linear systems \(g^1_k\) of type I and having no other linear systems \(g^1_k\). Taking into account that there is no 4-gonal curve of genus 7 having exactly two linear systems \(g_4^1\) both being of type I, this result is complete. The proof of the theorem is by means of induction on \(g\). The induction starts with a general \((k-1)\)-gonal curve of genus \(2k-1\).
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 1031532
zbMATH Keywords: curves possessing exactly two linear systems
MaRDI profile type: Publication
full work available at URL: s002080050034
OpenAlex ID: W2002546456
DOI: 10.1007/S002080050034
author: Marc Coppens
Recommended article: On singularities of the curves belonging to some linear systems in \({\mathbb{P}}^ 2\)
Recommended article: Linear systems of plane curves through fixed ''fat'' points of \(\mathbb{P}^ 2\)
Recommended article: Linear syzygies of curves with prescribed gonality
Recommended article: Q3202239
Recommended article: Q4383390
Recommended article: Q4295829
Recommended article: Q3100283
Recommended article: Smooth curves possessing many linear systems \(g^ 1_ n\)
Recommended article: Q3418291
description: scientific article; zbMATH DE number 1031532