Corrigendum to: ``Compactifications of \(\mathbb{C}^ 3\). II''
type: Item
instance of: scholarly article
title: Corrigendum to: ``Compactifications of \(\mathbb{C}^ 3\). II''
zbMATH Open document ID: 0799.14021
DOI: 10.1007/BF01459518
author: Thomas Peternell
published in: Mathematische Annalen
publication date: 1994-04-12T00:00:00Z
review text: In the paper cited in the title [ibid. 283, No. 1, 121-137 (1989; Zbl 0671.14020)], I studied algebraic compactifications \(X\) of \(\mathbb{C}^ 3\) with second Betti number 1 (which are necessarily Fano manifolds) and nonnormal divisor at infinity \(Y\). The main result was the following: If the index of \(X\) is 1, then its genus is 12, in particular \(X\) is rational with \(b_ 3 = 0\). In the proof however there is a gap as pointed out by \textit{Furushima}. The aim of this note is to show how to complete the proof.
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 537332
zbMATH Keywords: Fano threefold
zbMATH Keywords: algebraic compactification of complex 3-space
MaRDI profile type: Publication
cites work: Q3957221
cites work: Compactifications of \({\mathbb{C}}^ 3\). II
full work available at URL: https://doi.org/10.1007/bf01459518
OpenAlex ID: W4247210989
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description: scientific article; zbMATH DE number 537332