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.
Gilberto Bini, Robert Laterveer, Gianluca Pacienza (2019). Voisin's Conjecture for 0-cycles on Calabi-Yau varieties and their mirror. ADVANCES IN GEOMETRY, 20(1), 91-108 [10.1515/advgeom-2019-0008].
Voisin's Conjecture for 0-cycles on Calabi-Yau varieties and their mirror
Gilberto Bini;
2019-01-01
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.
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MVEC40-[Advances in Geometry] Voisins conjecture for zero-cycles on CalabiYau varieties and their mirrors.pdf
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