Compactifications of \({\mathbb{C}}^ 3\). II
type: Item
instance of: scholarly article
title: Compactifications of \({\mathbb{C}}^ 3\). II
zbMATH Open document ID: 0671.14020
DOI: 10.1007/BF01457505
author: Thomas Peternell
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164497
review text: [For part I of this paper see the author and \textit{M. Schneider}, Math. Ann. 280, No.1, 129-146 (1988; Zbl 0651.14025).] This paper shows that Fano compactifications of \({\mathbb{C}}^ 3\) with \(b_ 2=1\) and index \(r=1\) have genus \(g(:=+(c^ 3_ 1/2)+1)=12\), and are thus rational with \(b_ 3=0\). The proof rests on the classification of Fano threefolds of Iskovskij-Shokurov. Such a compactification exists, as shown by M. Furushima. Fano compactifications with \(b_ 2=1\) and (4\(\geq)r\geq 2\) are classified in part I of this paper. Other papers with \textit{S. Kosarew} show that compactifications of \({\mathbb{C}}^ 3\) with \(b_ 2=1\) are Moishezon.
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 4097548
zbMATH Keywords: Fano compactifications of complex 3-space
zbMATH Keywords: Fano threefolds
reviewed by: Frédéric Campana
MaRDI profile type: Publication
cites work: Introduction to Grothendieck duality theory
cites work: Complex analytic geometry
cites work: Q3818432
cites work: Threefolds whose canonical bundles are not numerically effective
cites work: Compactifications of \({\mathbb{C}}\) 3. I
cites work: Q3778856
OpenAlex ID: W2912642324
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description: scientific article; zbMATH DE number 4097548