Bloch's conjecture for Catanese and Barlow surfaces

Claire Voisin

Bloch's conjecture for Catanese and Barlow surfaces

Algebraic Geometry 2015-06-30 v2

Authors: Claire Voisin

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.

Keywords

del pezzo surfaces algebraic surfaces

Cite

@article{arxiv.1210.3935,
  title  = {Bloch's conjecture for Catanese and Barlow surfaces},
  author = {Claire Voisin},
  journal= {arXiv preprint arXiv:1210.3935},
  year   = {2015}
}

Comments

Title changed. The surfaces studied in the paper are Catanese surfaces (or numerical Campedelli surfaces), They are not the Campedelli surfaces

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