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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


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Voisin’s conjecture for zero-cycles on Calabi–Yau varieties and their mirrors

Gilberto Bini
  • Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
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/ Robert Laterveer
  • Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, 67084, Strasbourg, CEDEX, France
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/ Gianluca Pacienza
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  • Institut Élie Cartan de Lorraine à Nancy, Université de Lorraine, B.P. 70239, Vandoeuvre-lès-Nancy CEDEX, France
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Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2019-0008

Abstract

We study a conjecture, due to Voisin, on 0-cycles on varieties with pg = 1. Using Kimura’s finite dimensional motives and recent results of Vial’s on the refined (Chow–)Künneth decomposition, we provide a general criterion for Calabi–Yau manifolds of dimension at most 5 to verify Voisin’s conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to 5.

Keywords: Algebraic cycles; Chow groups; motives; finite-dimensional motives; Calabi–Yau varieties

MSC 2010: Primary 14C15; 14C25; 14C30

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About the article

Received: 2017-10-19

Revised: 2018-01-04

Published Online: 2019-09-11


Communicated by: I. Coskun


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0008.

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