Algebraic cycles on certain Calabi-Yau threefolds
type: Item
instance of: scholarly article
title: Algebraic cycles on certain Calabi-Yau threefolds
zbMATH Open document ID: 0791.14017
DOI: 10.1007/BF02571731
author: Fabio Bardelli
author: Stefan Müller-Stach
published in: Mathematische Zeitschrift
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/174629
review text: The authors propose a method to study the Griffiths group of codimension two cycles on Calabi-Yau 3-folds \(X\) that are complete intersections in some ambient variety \(Y\). Surfaces in the Noether-Lefschetz locus of codimension two cycles on \(Y\) are used to produce interesting cycles on \(X\) by intersection. The Abel-Jacobi invariants of these cycles are studied by an infinitesimal method. In particular it is shown that under certain assumptions on the geometry of the components in the Noether- Lefschetz locus this construction is sufficient to generate an infinite dimensional subspace of the rational Griffiths group. For certain families of Calabi-Yau 3-folds, including the intersection of two general cubics, this is explicitly verified.
reviewed by: Stefan Müller-Stach
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 567463
zbMATH Keywords: Griffiths group
zbMATH Keywords: codimension two cycles
zbMATH Keywords: Calabi-Yau 3-folds
zbMATH Keywords: Noether- Lefschetz locus
zbMATH Keywords: Abel-Jacobi invariants
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 567463