A criterion for the canonical bundle of a 3-fold to be ample
type: Item
instance of: scholarly article
title: A criterion for the canonical bundle of a 3-fold to be ample
zbMATH Open document ID: 0596.14008
DOI: 10.1007/BF01456985
author: Kenji Matsuki
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164220
review text: We show that the (anti-)canonical bundle of a complete normal 3-fold with only canonical singularities is ample if and only if it is numerical positive. If we put a stronger assumption \(\kappa (X)>0\) as P. M. H. Wilson did in his original proof of the theorem, then the assertion is an immediate consequence of Kawamata's base point free theorem. The essential difficulty to prove the above theorem is to exclude the worst possible case \(\kappa (X)=0\), which we overcome using the classification of normal surfaces due to F. Sakai in connection with the abundance conjecture.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 3959615
zbMATH Keywords: numerically positive bundle of a complete normal 3-fold
zbMATH Keywords: ampleness
MaRDI profile type: Publication
cites work: Rationalité des singularités canoniques
cites work: Pluricanonical systems on minimal algebraic varieties
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cites work: Q3825176
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cites work: Maximal subbundles of vector bundles on a curve
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OpenAlex ID: W1980634929
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description: scientific article; zbMATH DE number 3959615