Global smoothing of Calabi-Yau threefolds
type: Item
instance of: scholarly article
title: Global smoothing of Calabi-Yau threefolds
zbMATH Open document ID: 0861.14036
DOI: 10.1007/BF01231450
author: Yoshinori Namikawa
author: Jozef Steenbrink
published in: Inventiones Mathematicae
publication date: 1996-05-13T00:00:00Z
full work available at URL: https://eudml.org/doc/144326
review text: Let \(Z\) be a Calabi-Yau threefold, i.e. a projective threefold with only rational singularities and with \(K_Z \sim 0\). Assume that \(Z\) admits only isolated rational hypersurface singularities. Then \(Z\) can be deformed to a Calabi-Yau threefold \(Z'\) with only ordinary double points; \(Z'\) is smooth if \(Z\) is \(\mathbb{Q}\)-factorial. Furthermore if \(X\) is a normal projective threefold with only isolated rational hypersurface singularities and \(h^2(X, {\mathcal O}_X) =0\), then the rank of the abelian group of Weil divisors of \(X\) modulo the Cartier ones is expressed in terms of the Betti numbers for the singular cohomology of \(Z\). The smoothing problems here considered are faced by two different ways: one using the vanishing theorems by Guillèn, Navarro Aznar and Puerto; the other using an invariant introduced by the first author for an isolated rational singularity.
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 861969
zbMATH Keywords: Calabi-Yau threefold
zbMATH Keywords: rational hypersurface singularities
reviewed by: Marino Palleschi
Wikidata QID: Q60961647
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 861969