Log abundance theorem for threefolds
type: Item
instance of: scholarly article
title: Log abundance theorem for threefolds
zbMATH Open document ID: 0818.14007
DOI: 10.1215/S0012-7094-94-07504-2
author: Sean Keel
author: Kenji Matsuki
author: James McKernan
published in: Duke Mathematical Journal
publication date: 1995-08-08T00:00:00Z
review text: The abundance theorem of Y. Kawamata and Y. Miyaoka states that the canonical divisor, of a minimal model of a threefold -- an endproduct of the minimal model program of Mori -- is semiample. In this paper, the abundance theorem is generalized for the log-extension of the minimal model program due to Shokurov. The log-abundance theorem, proved by the authors of this paper, states: Let the pair \((X,D)\) consist of a threefold \(X\) and a boundary \(D\) (i.e., \(D\) is a \(\mathbb{Q}\)-Weil divisor, such that any irreducible component \(D_ i\) of \(D\) has multiplicity \(d_ i \in [0,1])\), and let \(K_ X + D\) be nef and log-canonical. Then some integer multiple of \(K_ X + D\) is base-point free.
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 706708
zbMATH Keywords: semiample canonical divisor
zbMATH Keywords: base-point freeness of divisor
zbMATH Keywords: abundance theorem
zbMATH Keywords: minimal model program
zbMATH Keywords: log-abundance theorem
zbMATH Keywords: threefold
reviewed by: Atanas Iliev
MaRDI profile type: Publication
Wikidata QID: Q101096146
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full work available at URL: s0012-7094-94-07504-2
OpenAlex ID: W1990861383
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description: scientific article; zbMATH DE number 706708