The cone of curves of algebraic varieties
type: Item
instance of: scholarly article
title: The cone of curves of algebraic varieties
zbMATH Open document ID: 0544.14009
DOI: 10.2307/2007087
author: Yujiro Kawamata
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1195515320
review text: In this paper two of the four steps are proved toward the theory of minimal models of algebraic varieties according to the program of M. Reid; we have proved: (1) the cone theorem; (2) the contraction theorem, and there remains: (3) the flip conjecture; (4) the induction conjecture. - \textit{J. Kollár} [ibid. 120, 1-5 (1984; see the following review)] proved the discreteness of the extremal rays and completed the picture of the cone. We note here that our theorems are easily generalised to the relative case starting from a projective morphism \(f:X\to S\) instead of a projective variety X.
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 3865464
zbMATH Keywords: cone of curves
zbMATH Keywords: vanishing theorem
zbMATH Keywords: minimal models of algebraic varieties
zbMATH Keywords: contraction theorem
MaRDI profile type: Publication
OpenAlex ID: W2334032522
description: scientific article; zbMATH DE number 3865464