Fundamental groups of elliptic fibrations and the invariance of the plurigenera for surfaces with odd first Betti number
type: Item
instance of: scholarly article
title: Fundamental groups of elliptic fibrations and the invariance of the plurigenera for surfaces with odd first Betti number
zbMATH Open document ID: 1077.14047
author: Markus Dürr
published in: Expositiones Mathematicae
publication date: 2005-06-13T00:00:00Z
review text: In the paper under review, the author studies the fundamental group of an elliptic surface and the close relationship between the Kodaira dimension of an elliptic surface with odd first Betti number and the geometry of its base orbifold. It is proved that every elliptic fibration \(X \to C\) with trivial first direct image sheaf can be obtained from a product \(C \times E\), where \(E\) is an elliptic curve, by means of logarithmic transformations. The fundamental groups of such an elliptic fibration is computed. In addition, the author presents a new and much shorter proof to the fact that the plurigenera and hence the Kodaira dimension of a complex surface with odd first Betti number are determined by the isomorphism type of the fundamental group.
reviewed by: Zhenbo Qin
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 14J80
Mathematics Subject Classification ID: 14F35
zbMATH DE Number: 2175359
MaRDI profile type: Publication
full work available at URL: j.exmath.2005.01.008
OpenAlex ID: W2031472842
Wikidata QID: Q114179702
cites work: Q5749404
cites work: Q4296322
cites work: Q4289665
cites work: On the Structure of Compact Complex Analytic Surfaces, I
cites work: Q4145882
cites work: Stable bundles with torsion Chern classes on non-Kählerian elliptic surfaces
cites work: The Geometries of 3-Manifolds
cites work: Q4337982
DOI: 10.1016/J.EXMATH.2005.01.008
description: scientific article; zbMATH DE number 2175359