On the Donaldson polynomials of elliptic surfaces
type: Item
instance of: scholarly article
title: On the Donaldson polynomials of elliptic surfaces
zbMATH Open document ID: 0807.57016
DOI: 10.1007/BF01459803
published in: Mathematische Annalen
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165227
review text: The Donaldson invariants of smooth simply connected minimal elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\) are polynomials in the intersection form \(q\) and canonical class \(k\). We compute, using Donaldson-Floer theory, the second nonzero coefficient in their expansion in \(q\) and \(k\) when the geometric genus is odd. We point out how this result (recently obtained also by Morgan and Mrowka, using different methods, for any geometric genus) yields the classification of smooth simply connected elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\) up to diffeomorphism.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 14J15
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 57R55
zbMATH DE Number: 683118
zbMATH Keywords: classification of smooth simply connected elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\)
zbMATH Keywords: Donaldson invariants of smooth simply connected minimal elliptic surfaces
zbMATH Keywords: Donaldson-Floer theory
author: Paolo Lisca
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 683118