Holomorphic vector fields and Chow groups

2019/11/12 by Wenchuan Hu, Hu, Wenchuan
Mathematics · #14C15 #14F43 #32M25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1911.04701

openalex publication_date 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the chow group of p-cycles with rational coefficients are isomorphic to the corresponding rational homology groups for smooth complex projective varieties carrying a holomorphic vector field with an isolated zero locus. As applications, we obtain Chow groups and Lawson homology groups with rational coefficients and verify the Friedlander-Mazur conjecture and the Generalized Hodge conjecture for those varieties.

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