Neron-Severi group for nonalgebraic elliptic surfaces. I: Elliptic bundle case
type: Item
instance of: scholarly article
title: Neron-Severi group for nonalgebraic elliptic surfaces. I: Elliptic bundle case
zbMATH Open document ID: 0847.32032
DOI: 10.1007/BF02568338
author: Vasile Brînzănescu
published in: Manuscripta Mathematica
publication date: 1994-01-31T00:00:00Z
full work available at URL: https://eudml.org/doc/155834
review text: The Néron-Severi group of elliptic bundles over a curve is studied. An elliptic bundle \(X \to B\) is a principal fiber bundle over a complex, compact, connected smooth curve \(B\) whose typical fiber and structure group are an elliptic curve \(E\). Denote by \(E_B\) the sheaf of germs of local holomorphic maps from \(B\) to \(E\) and consider the cohomology class \(\xi\) in \(H^1 (E_B)\) which defines the elliptic bundle \(X \to B\). The author proves that, if \(c(\xi) \neq 0\), the group \(NS(X)/ \text{Tors} NS (X)\) is isomorphic to the group of morphisms of abelian varieties \(\Hom (J_B,E)\), where \(J_B\) denotes the Jacobian variety of \(B\). Moreover, also in case \(c(\xi) = 0\), the author determines the rank of the Néron-Severi group in terms of the genus and of the period matrix of the curve \(B\).
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 492817
zbMATH Keywords: Néron-Severi group
zbMATH Keywords: elliptic bundles over a curve
zbMATH Keywords: group of morphisms of abelian varieties
zbMATH Keywords: Jacobian variety
reviewed by: Cristina Turrini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492817