A counterexample to the Hodge conjecture for Kaehler varieties

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dc.creatorVoisin, Claire
dc.date2001-12-21
dc.date.accessioned2026-07-07T10:10:01Z
dc.date.available2026-07-07T10:10:01Z
dc.descriptionSummary: 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.
dc.descriptionLatex
dc.identifierhttps://arxiv.org/abs/math/0112247
dc.identifierhttp://arxiv.org/abs/math/0112247
dc.identifierInt. Math. Res. Not. 2002, no. 20, 1057--1075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171500
dc.subjectAlgebraic Geometry
dc.titleA counterexample to the Hodge conjecture for Kaehler varieties
dc.typetext

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