Transcendence degree of zero-cycles and the structure of Chow motives

Sergey Gorchinskiy, Vladimir Guletskii

Published 2010-09-08, updated 2010-11-28Version 2

We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular interest in the context of Bloch's conjecture, especially for Godeaux surfaces, when the surface is given as a finite quotient of a suitable quintic in P^3.