An example of two homeomorphic, nondiffeomorphic complete intersection surfaces
type: Item
instance of: scholarly article
title: An example of two homeomorphic, nondiffeomorphic complete intersection surfaces
zbMATH Open document ID: 0707.14045
DOI: 10.1007/BF01234435
author: Wolfgang Ebeling
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143774
review text: Let \(d_ i\in {\mathbb{N}}\), \(d_ i\geq 2\), \(i=1,...,r\). A complete intersection surface of multidegree \((d_ 1,...,d_ r)\) is a nonsingular algebraic surface \(S(d_ 1,...,d_ r)\subset {\mathbb{C}}{\mathbb{P}}^{r+2}\) which is the transversal intersection of r hypersurfaces of degree \(d_ 1,...,d_ r,\) respectively. Any two complete intersection surfaces with the same multidegree are diffeomorphic. The author proves (by using results of Freedman, Donaldson, Friedman and Morgan) that \(S(10,7,7,6,3,3)\subset {\mathbb{C}}{\mathbb{P}}^ 8\) and \(S(9,5,3,3,3,3,3,2,2)\subset {\mathbb{C}}{\mathbb{P}}^{11}\) are homeomorphic, but not diffeomorphic.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4160946
zbMATH Keywords: homeomorphism
zbMATH Keywords: diffeomorphism
zbMATH Keywords: complete intersection surface
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4160946