Torsion cohomology classes and algebraic cycles on complex projective manifolds

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Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincaré dual to an algebraiccycle. We notice that the order ofthese classes are small comparedto the dimension of the manifold.However, building upon a construction ofKollàr, one can provide such examples witharbitrary high prime order, the dimension being fixed. This method alsoprovides examples of torsion algebraiccycles, which are non trivial in the Griffiths' groups, and lie in a arbitrary high level of the H.Saito filtration onChow groups.
Final version, to appear in Adv. in Mathematics, special issue dedicated to M. Artin. References to related work by C. Schoen added. A mistake mentioned by K. O'Grady corrected

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Algebraic Geometry, 14C25, 14C30, 14C35

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http://salesiana.dossiersoluciones.com/handle/123456789/70470

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403254
 http://arxiv.org/abs/math/0403254

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arXiv