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

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

2006-02-23

arxiv.org/abs/math/0602516v2

Mathematics

Algebraic Geometry

6 pages, add a remark and a reference

Scientific paper

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\leq p\leq s. We show that the homologically trivial sector of rational Lawson homology L_pH_k(X,Q)_{hom} vanishes for 0\leq n-p\leq 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 Ch_0(X) =Z.

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