Inversion of abelian integrals
type: Item
instance of: scholarly article
title: Inversion of abelian integrals
zbMATH Open document ID: 0642.14005
DOI: 10.1007/BF01261980
author: Montserrat Teixidor i Bigas
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Given a projective non-singular curve of genus g and an integer \(k\geq 2g- 1\), the natural map from the k-symmetric product of the curve to the jacobian is a projective bundle. The pull-back of this bundle to the universal cover of the jacobian is trivial and it should be possible to describe the bundle by means of multiplicative factors. This is the problem of inversion of abelian integrals proposed by Kempf. In this paper, an explicit description of the bundle is given (in case \(k=2g-1)\) in terms of trivializing sets and transition functions. This generalizes a result of \textit{K. R. Coombes} and \textit{R. J. Fisher} [Math. Ann. 275, 185-196 (1986; Zbl 0579.14023)] which deals only with the cases \(g=2\) and \(g=3\) for non-hyperelliptic curves.
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14K05
zbMATH DE Number: 4045916
zbMATH Keywords: non-singular curve of genus g
zbMATH Keywords: jacobian
zbMATH Keywords: inversion of abelian integrals
MaRDI profile type: Publication
cites work: Q3347989
cites work: Q4108448
cites work: Inversion of Abelian integrals
full work available at URL: https://doi.org/10.1007/bf01261980
OpenAlex ID: W1983848434
description: scientific article; zbMATH DE number 4045916