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arXiv · 1210.3935

Bloch's conjecture for Catanese and Barlow surfaces

Claire Voisin
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Abstract

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.

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Claire Voisin. 2012-10-15. Bloch's conjecture for Catanese and Barlow surfaces. https://arxiv.org/abs/1210.3935

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