A special divisor on a double covering of a compact Riemann surface
type: Item
instance of: scholarly article
title: A special divisor on a double covering of a compact Riemann surface
zbMATH Open document ID: 0928.14008
author: Shigeo Mitsunari
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-09-12T00:00:00Z
review text: Let \(C\) denote a nonsingular, projective complex curve. If \(D\) is a divisor on \(C\), let \(c(D)=\deg D - 2 l(D) +2\) denote the Clifford index of \(D\). The author shows two results: (1) If \(C\) admits a special divisor with small Clifford index, then \(C\) is a two-sheeted cover of a curve with genus at most \(c(D)/2\), and (2) conversely, if \(C\) is a two-sheeted cover of a curve of genus \(g'\), then \(C\) has a special divisor \(D\) with \(c(D)=2g'\). The first result is very similar to a theorem proved by \textit{M. Coppens} and \textit{G. Martens} [Compos. Math. 78, No. 2, 193-212 (1991; Zbl 0741.14035)], while the second result is very similar to a theorem proved by \textit{F. Torres} [Manuscr. Math. 83, No. 1, 39-58 (1994; Zbl 0838.14025)].
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 1217278
zbMATH Keywords: special divisor
zbMATH Keywords: double covering
zbMATH Keywords: hyperelliptic curve
zbMATH Keywords: small Clifford index
reviewed by: Robert F. Lax
MaRDI profile type: Publication
full work available at URL: pjaa.74.61
OpenAlex ID: W2058303629
cites work: Q3347989
cites work: On the Clifford Index of Algebraic Curves
cites work: Varieties of special divisors on a curve. II.
cites work: Q4023939
cites work: Theta characteristics of an algebraic curve
DOI: 10.3792/PJAA.74.61
description: scientific article; zbMATH DE number 1217278