On Hard Lefschetz Conjecture on Lawson Homology

Details On Hard Lefschetz Conjecture on Lawson Homology On Hard Lefschetz Conjecture on Lawson Homology

2011-01-26

arxiv.org/abs/1101.4990v1

Mathematics

Algebraic Geometry

7 pages

Scientific paper

Friedlander and Mazur proposed a conjecture of hard Lefschetz type on Lawson homology. We shall relate this conjecture to Suslin conjecture on Lawson homology. For abelian varieties, this conjecture is shown to be equivalent to a vanishing conjecture of Beauville type on Lawson homology. For symmetric products of curves, we show that this conjecture amounts to the vanishing conjecture of Beauville type for the Jacobians of the corresponding curves. As a consequence, Suslin conjecture holds for all symmetric products of curves with genus at most 2.

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