Neron-Severi group for nonalgebraic elliptic surfaces. II: Non-Kählerian case
type: Item
instance of: scholarly article
title: Neron-Severi group for nonalgebraic elliptic surfaces. II: Non-Kählerian case
zbMATH Open document ID: 0854.32015
DOI: 10.1007/BF02567466
author: Vasile Brînzănescu
published in: Manuscripta Mathematica
publication date: 1994-12-18T00:00:00Z
full work available at URL: https://eudml.org/doc/156000
review text: The Neron-Severi group of a non-Kählerian elliptic surface \(\varphi : X \to B\) is studied. The paper is a continuation of part I: The elliptic bundle case, ibid. 79, No. 2, 187-195 (1993; Zbl 0847.32032) which deals with the Neron-Severi group of elliptic bundles. First the author shows that a non-Kählerian elliptic surface \(\varphi : X \to B\) has the structure of a quasi-bundle, which means that it is an elliptic bundle, except for some singular fibers which are multiples of smooth elliptic curves. Then he proves that given a quasi-bundle \(\varphi : X \to B\) with odd Betti numbers, there exists an elliptic bundle which is a cyclic cover of \(\varphi\). This enables him to use the above quoted part I and so to get the following isomorphism: \(NS (X) \times \mathbb{Q} \cong \Hom (J_B,E) \times \mathbb{Q}\), where \(J_B\) denotes the Jacobian variety of \(B,E\) the general fiber of \(\varphi\) and \(\Hom (J_B,E)\) denotes the group of the morphisms of abelian varieties.
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 14J27
zbMATH DE Number: 703893
zbMATH Keywords: Neron-Severi group
zbMATH Keywords: non-Kählerian elliptic surface
reviewed by: Cristina Turrini
MaRDI profile type: Publication
cites work: Q5749404
cites work: Neron-Severi group for nonalgebraic elliptic surfaces. I: Elliptic bundle case
cites work: The Picard group of a primary Kodaira surface
cites work: On the moduli spaces of surfaces of general type. Appendix: Letter of E. Bombieri written to the author
cites work: On the Structure of Compact Complex Analytic Surfaces, I
cites work: On compact analytic surfaces. II
cites work: Kähler metrics on elliptic surfaces
cites work: Q4090463
cites work: Abelian covers of algebraic varieties.
cites work: Multiple fibres of a morphism
cites work: The Picard group of a quasi-bundle
description: scientific article; zbMATH DE number 703893