On the Neron-Severi group of Jacobians of curves with automorphisms
type: Item
instance of: scholarly article
title: On the Neron-Severi group of Jacobians of curves with automorphisms
zbMATH Open document ID: 0803.14017
DOI: 10.1016/0019-3577(93)90004-I
author: Fabio Giovanetti
published in: Indagationes Mathematicae. New Series
publication date: 1994-12-15T00:00:00Z
review text: Let \(C\) be a smooth projective complex curve with a cyclic group of automorphisms of prime order. By using the well-known isomorphism between NS(J) (the Neron-Severi group of the jacobian of \(C)\) and the invariant part (under the Rosati involution) of its ring of endomorphisms, the author gives a geometric description of certain elements of NS(J) which allows him to estimate rank NS(J) from below. Then the author proves the main result which asserts that under certain hypotheses, about the eigenspaces of the space of holomorphic differentials, those found elements span NS(J).
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14H70
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 510028
zbMATH Keywords: cyclic group automorphisms
zbMATH Keywords: Neron-Severi group
zbMATH Keywords: Jacobian
zbMATH Keywords: ring of endomorphisms
reviewed by: A. Del Centina
MaRDI profile type: Publication
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full work available at URL: 0019-3577(93)90004-i
OpenAlex ID: W2079903056
description: scientific article; zbMATH DE number 510028