Voisin's Conjecture for Zero--cycles on Calabi--Yau Varieties and their\n Mirrors

2017/06/01 by Gilberto Bini, Bini, Gilberto, Robert Laterveer +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1706.00472

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a conjecture, due to Voisin, on 0-cycles on varieties with p_g=1.\nUsing Kimura's finite dimensional motives and recent results of Vial's on the\nrefined (Chow-)K "unneth decomposition, we provide a general criterion for\nCalabi-Yau manifolds of dimension at most 5 to verify Voisin's conjecture. We\nthen check, using in most cases some cohomological computations on the mirror\npartners, that the criterion can be successfully applied to various examples in\neach dimension up to 5.\n

Citations

• Arithmetic and Attractors
• Log homogeneous varieties

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