Some contractions of threefold algebraic family
type: Item
instance of: scholarly article
title: Some contractions of threefold algebraic family
zbMATH Open document ID: 0823.14024
DOI: 10.1142/S0252959999000278
author: Meng Chen
published in: Chinese Annals of Mathematics. Series B
publication date: 1994-09-19T00:00:00Z
review text: By the central result of the Mori theory, the possible extremal morphisms on a smooth projective threefold can be distinguished from each other by the numerical properties of their corresponding extremal curves and supporting divisors. In this paper the author studies special cases of threefolds of negative Kodaira dimension and with small Picard number, and finds which of the Mori extremal contractions are possible for these threefolds (theorems 2.2 and 2.3). The study is based on the known numerical properties of possible extremal curves, and on the generalization of the rationality theorem proved in the beginning (theorem 2.1), which imposes additional numerical restrictions on these extremal curves.
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 640445
zbMATH Keywords: Mori theory
zbMATH Keywords: threefold
zbMATH Keywords: negative Kodaira dimension
zbMATH Keywords: extremal contractions
zbMATH Keywords: extremal curves
zbMATH Keywords: rationality theorem
reviewed by: Atanas Iliev
MaRDI profile type: Publication
full work available at URL: s0252959999000278
OpenAlex ID: W2312961963
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description: scientific article; zbMATH DE number 640445