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

  • Gilberto Bini , Robert Laterveer and Gianluca Pacienza EMAIL logo
Published/Copyright: September 11, 2019
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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.

  1. Communicated by: I. Coskun

Acknowledgements

We wish to thank Giuseppe Ancona, Lie Fu, Bert van Geemen, Hossein Movasati, Roberto Pignatelli and Charles Vial for useful and stimulating exchanges related to this paper. We warmly thank Claire Voisin for pointing out a mistake in a previous version of the paper, and the referee for several helpful and highly pertinent remarks.

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Received: 2017-10-19
Revised: 2018-01-04
Published Online: 2019-09-11
Published in Print: 2020-01-28

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