A criterion for algebraicity of certain analytic elliptic surfaces
type: Item
instance of: scholarly article
title: A criterion for algebraicity of certain analytic elliptic surfaces
zbMATH Open document ID: 0835.14014
DOI: 10.1007/BF01461015
author: Mitsuru Kawazoe
published in: Mathematische Annalen
publication date: 1996-04-15T00:00:00Z
full work available at URL: https://eudml.org/doc/165391
review text: Let \(f : S \to C\) be a compact complex analytic elliptic surface obtained by logarithmic transformations from a trivial elliptic fibration over a nonsingular algebraic curve \(C\). In this paper, the author proves that the algebraicity of \(S\) is equivalent to the existence of a meromorphic 1-form on \(C\) which satisfies some conditions. Furthermore, the author obtains the result that when the genus of \(C\) is greater than or equal to 1, the algebraicity of \(S\) is closely related to the relation between points over which the elliptic fibration has multiple fibres.
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 32J99
Mathematics Subject Classification ID: 14D99
zbMATH DE Number: 840210
zbMATH Keywords: analytic elliptic surface
zbMATH Keywords: algebraicity
zbMATH Keywords: elliptic fibration
MaRDI profile type: Publication
cites work: On compact analytic surfaces. II
cites work: On the Structure of Compact Complex Analytic Surfaces, I
cites work: On elliptic surfaces in characteristic p
cites work: Extension theorems for Kähler metrics
description: scientific article; zbMATH DE number 840210