Smoothable varieties with torsion free canonical sheaf
type: Item
instance of: scholarly article
title: Smoothable varieties with torsion free canonical sheaf
zbMATH Open document ID: 0683.14013
DOI: 10.1007/BF01173698
author: Donu Arapura
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155364
review text: Let X be a d-dimensional smoothable Cohen-Macaulay projective variety. Consider the canonical map \(c:\quad \Omega^ d_ X\to \omega_ X.\) Let L be an ample line bundle on X. By a clever calculation involving \(\chi (\Omega^ d_ X\otimes L^ N)\) for \(N\gg 0\), the author shows that if c is injective, then c is an isomorphism and X is smooth by a theorem of Kunz and Waldi.
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4118498
zbMATH Keywords: smoothable Cohen-Macaulay projective variety
reviewed by: Lawrence Ein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4118498