Log models of birationally rigid varieties
type: Item
instance of: scholarly article
title: Log models of birationally rigid varieties
zbMATH Open document ID: 1016.14005
DOI: 10.1007/BF02984105
published in: Journal of Mathematical Sciences (New York)
publication date: 2001-01-16T00:00:00Z
review text: Let \(X\) be a projective manifold \(X\) of dimension \(n\geq 2\). From the point of view of the Mori theory one of the important points in understanding the birational geometry of \(X\) is the problem of describing all the Mori spaces which are birationally isomorphic to \(X\). Recall that a Mori space is a morphism \(f:Z\to S\), where \(Z\) is a projective variety having at most terminal \(\mathbb Q\)-factorial singularities, with \(f\)-ample anticanonical class and one-dimensional relative Picard group, and \(S\) is a normal projective variety of dimension smaller than the dimension of \(Z\) such that \(f_*(\mathcal O_Z)=\mathcal O_S\). In the paper under review the author uses the concept of movable log pairs \((X,M)\) (where \(M=\sum_ib_iM_i\), with \(b_i\) nonnegative rational numbers and \(M_i\) linear systems on \(X\) without fixed components) to study this question, in fact to classify all log models of a given projective manifold \(X\). His idea is to translate the existence of log pairs into numerical constraint of the linear system. Some of the results obtained generalize known results for \(3\)-folds.
reviewed by: Lucian Bădescu
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 1551881
zbMATH Keywords: birarionally rigid varieties
zbMATH Keywords: Mori spaces
zbMATH Keywords: movable log pairs
author: I. A. Cheltsov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1551881