On the Abel-Jacobi map for non-compact varieties
type: Item
instance of: scholarly article
title: On the Abel-Jacobi map for non-compact varieties
zbMATH Open document ID: 0929.14017
author: Donu Arapura
author: Kyungho Oh
published in: Osaka Journal of Mathematics
publication date: 1999-08-05T00:00:00Z
review text: Let \(X/\mathbb{C}\) be a smooth projective curve, \(S\) a reduced divisor on \(X\), \(J(X\setminus S)\) the generalized jacobian of \(X\setminus S\) and \(\text{Div}^0(X\setminus S)\) the set of divisors of degree \(0\) which do not intersect with \(S\). By integration one determines the Abel-Jacobi homomorphism \(\alpha:\text{Div}^0(X\setminus S)\to J(X\setminus S)\). The authors prove that \(\text{Ker} \alpha\) is the subgroup of \(S\)-principal divisors: \[ \text{Prin}_S(X)=\{(f)\in\text{Div}(X\setminus S):f\in K(X),\;f=1\text{ on }S\}. \] {}.
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 1132988
zbMATH Keywords: non-compact varieties
zbMATH Keywords: generalized Jacobian
zbMATH Keywords: Abel-Jacobi homomorphism
reviewed by: Giuseppe Tomassini
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1132988