Elementary contractions of algebraic 3-folds
type: Item
instance of: scholarly article
title: Elementary contractions of algebraic 3-folds
zbMATH Open document ID: 0542.14007
DOI: 10.2307/2006964
author: Yujiro Kawamata
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
review text: This paper gives proofs of some steps toward the theory of minimal models of algebraic 3-folds. Let X be an algebraic 3-fold which admits some mild singularities. Then the theorems are: (1) The closed cone of curves on X is generated by extremal rays in the half space \(K_ X<0\). (2) An extremal ray can be contracted by a morphism from X. - The proof uses a result previously obtained by the author in the paper ''On the finiteness of generators of a pluri-canonical ring for a 3-fold of general type'' (Am. J. Math.; to appear). A generalization to higher dimensional case is obtained in Ann. Math., II. Ser. 119, 603-633 (1984; Zbl 0544.14009).
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 3861312
zbMATH Keywords: minimal models of algebraic 3-folds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2006964
OpenAlex ID: W2030192217
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description: scientific article; zbMATH DE number 3861312