A counterexample to the Hodge conjecture for Kaehler varieties

Details A counterexample to the Hodge conjecture for Kaehler varieties A counterexample to the Hodge conjecture for Kaehler varieties

2001-12-21

arxiv.org/abs/math/0112247v1

Int. Math. Res. Not. 2002, no. 20, 1057--1075

Mathematics

Algebraic Geometry

Latex

Scientific paper

Summary: The Hodge conjecture asks whether rational Hodge classes on a smooth projective manifolds are generated by the classes of algebraic subsets, or equivalently by Chern classes of coherent sheaves. On a compact Kaehler manifold, Hodge conjecture is known to be false if algebraic subsets are replaced with analytic subsets. Here we show that it is even false that for a Kaehler manifold, Hodge classes are generated by Chern classes of coherent sheaves. We also show that finite free resolution do not in general exist for coherent sheaves on compact Kaehler manifolds.

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