A note on Lawson homology for smooth varieties with small Chow groups

2006/02/23 by Wenchuan Hu, Hu, Wenchuan
Mathematics · Physics and Astronomy · Computer Science · #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0602516

Abstract

Let X be a smooth projective variety of dimension n on which rational and homological equivalence coincide for algebraic p-cycles in the range 0≤ p≤ s. We show that the homologically trivial sector of rational Lawson homology L_pH_k(X,Q)_hom vanishes for 0≤ n-p≤ s+2. This is an analogue of a theorem of C. Peters in "dual dimensions". Together with Peters' theorem we get that the natural transformation L_pH_k(X,Q)--> H_k(X,Q) is injective for all p and k when X is a smooth projective variety of dimension 4 and Ch₀(X) =Z.

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