2004/03/16 by Christophe Soulé, C. Soule, Soule, C. +2 · 1 citation
Mathematics · #14C25 #14C30 #14C35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14C25 #msc:14C30 #msc:14C35
paper · pdf · doi:10.48550/arxiv.math/0403254
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
openalex publication_date 2004/03/16 · arxiv created 2005/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.