Universal Chow group of zero-cycles on cubic hypersurfaces
Universal Chow group of zero-cycles on cubic hypersurfaces
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Claire Voisin , Centre national de la recherche scientifique; Distinguished Visiting Professor, School of 外网天堂
Please note special day and time. 听We discuss the universal triviality of the听CH0-group of cubic hypersurfaces, or equivalently the existence of a Chow-theoretic decomposition of their diagonal. The motivation is the study of stable irrationality for these varieties. Our main result is that this decomposition exists if and only if it exists on the cohomological level. As an application, we find that a cubic threefold has universally trivial听CH0听group if and only if the minimal class听胃4/4!听of its intermediate jacobian is the class of a 1-cycle (only twice this class is known to be algebraic).