Geometric representability of 1-cycles on rationally connected threefolds

2022/08/26 by Claire Voisin, Voisin, Claire · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2208.12557

openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any rationally connected threefold X, there exists a smooth projective surface S and a family of 1-cycles on X parameterized by S, inducing an Abel-Jacobi isomorphism \rm Alb(S)≅ J³(X). This statement was previously known for some classes of smooth Fano threefolds.

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