Some remarks on the study of good contractions
type: Item
instance of: scholarly article
title: Some remarks on the study of good contractions
zbMATH Open document ID: 0860.14009
DOI: 10.1007/BF02570480
published in: Manuscripta Mathematica
publication date: 1997-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/156093
review text: Let \(X\) be a complex projective variety with log terminal singularities. A good contraction is a map \(\varphi: X\to Z\) onto a normal variety with connected fibres, such that the \(\mathbb{Q}\)-canonical divisor \(-K_X\) is \(\varphi\)-ample. In this case there exist a \(\varphi \)-ample line bundle \(L\) and a rational number \(r\) such that \(K_X + rL\) is the pullback of a line bundle of \(Z\). In this note the author studies the structure of \(\varphi\), proving in particular that for any fiber \(F:\) \(\dim F \geq r-1\) (and \(\dim F \geq r\) if \(\varphi\) is birational).
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J45
zbMATH DE Number: 784080
zbMATH Keywords: log terminal singularities
zbMATH Keywords: good contraction
zbMATH Keywords: pullback of a line bundle
author: Marco Andreatta
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784080