The existence of varieties whose hyperplane section is \({\mathbb{P}}^ r\)- bundle
type: Item
instance of: scholarly article
title: The existence of varieties whose hyperplane section is \({\mathbb{P}}^ r\)- bundle
zbMATH Open document ID: 0732.14003
author: Heinz Spindler
author: Ei-ichi Sato
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: There are two main results of the paper. In the first one the authors give sufficient conditions for a projective surface S and a vector bundle F on S, under which the projective bundle \({\mathbb{P}}(F)\) associated with F is an ample divisor in a smooth projective variety. - In the second one they also give sufficient conditions for a smooth projective variety S, under which any sequence \(\{A_ i\}\) of smooth projective varieties terminates, where \(A_ i\) is an ample divisor in \(A_{i+1}\), \(i=1,2,...\), and \(A_ 1\) is a \({\mathbb{P}}^ r\)-bundle over S. Although the authors work over an algebraically closed field of any characteristic, the above-mentioned results are in characteristic zero.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 4210308
zbMATH Keywords: vector bundle
zbMATH Keywords: ample divisor
zbMATH Keywords: projective variety
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520030
OpenAlex ID: W1576283419
DOI: 10.1215/KJM/1250520030
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description: scientific article; zbMATH DE number 4210308