The gonality and the Clifford index of curves on an elliptic ruled surface
type: Item
instance of: scholarly article
title: The gonality and the Clifford index of curves on an elliptic ruled surface
zbMATH Open document ID: 1068.14034
author: Takeshi Harui
published in: Archiv der Mathematik
publication date: 2005-04-14T00:00:00Z
review text: Let \(S\) be a geometrically ruled surface (i.e. a \(\mathbb P^1\)-bundle) over an elliptic curve \(C\) and \(X \subset S\) a smooth curve. Here the author for almost all numerical classes is able to explicitly compute the gonality and the Clifford index of \(X\). For the case of \(\mathbb P^1\)-bundles over \(\mathbb P^1\) (even for singular curves), see [\textit{G. Martens}, Arch. Math. 67, 349--352 (1996; Zbl 0872.14022)]. In most cases these invariants are computed using the ruling of \(S\), but the author found several exceptional cases.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14H51
Mathematics Subject Classification ID: 14J26
zbMATH DE Number: 2155975
zbMATH Keywords: \(\mathbb P^1\)-bundle over an elliptic curve
zbMATH Keywords: geometrically ruled surface
MaRDI profile type: Publication
full work available at URL: s00013-004-1140-x
OpenAlex ID: W2081065947
DOI: 10.1007/S00013-004-1140-X
description: scientific article; zbMATH DE number 2155975