The smooth classification of elliptic surfaces with \(b^ +>1\)
type: Item
instance of: scholarly article
title: The smooth classification of elliptic surfaces with \(b^ +>1\)
zbMATH Open document ID: 0828.14020
DOI: 10.1215/S0012-7094-94-07501-7
author: Zoltán Szabó
author: András I. Stipsicz
published in: Duke Mathematical Journal
publication date: 1996-01-08T00:00:00Z
review text: A compact complex surface \(S\) is elliptic if there is a holomorphic map \(\pi : S \to C\), where \(C\) is a complex curve and the generic fiber is a smooth elliptic curve. In this interesting paper the authors study the case \(C = \mathbb{C} \mathbb{P}^1\) and construct a family \({\mathcal I}\), such that every minimal elliptic surface (fibered over \(\mathbb{C} \mathbb{P}^1)\) is equivalent up to a deformation to an element of \({\mathcal I}\). The family \({\mathcal I}\) is built using a basic example (blow up the nine base points of a generic pencil of cubic curves in \(\mathbb{C} \mathbb{P}^2)\) and two operations. The first one is an appropriate fiber sum and the second is the logarithmic transformation. The main result depends on the computation of some nontrivial coefficients of the Donaldson polynomial of an elliptic surface.
reviewed by: F.Gherardelli
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 32J15
zbMATH DE Number: 706705
zbMATH Keywords: minimal elliptic surface
zbMATH Keywords: deformation
zbMATH Keywords: Donaldson polynomial
MaRDI profile type: Publication
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full work available at URL: s0012-7094-94-07501-7
OpenAlex ID: W2086410519
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description: scientific article; zbMATH DE number 706705