%0 Journal Article
%T Bloch's conjecture for Catanese and Barlow surfaces
%A Claire Voisin
%J Mathematics
%D 2012
%I arXiv
%X Catanese surfaces are regular surfaces of general type with $p_g=0$. They specialize to double covers of Barlow surfaces. We prove that the $CH_0$ group of a Catanese surface is equal to $\mathbb{Z}$, which implies the same result for the Barlow surfaces. We will also give a conditional application (more precisely, assuming the variational Hodge conjecture) of the same method to the Chow motive of low degree $K3$ surfaces.
%U http://arxiv.org/abs/1210.3935v2