Bloch's conjecture for Catanese and Barlow surfaces

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 $C{H}_0$ 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.

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

References in corpus (3)

• Determinantal Barlow surfaces and phantom categories
• Symplectic involutions of K3 surfaces act trivially on CH_0
• Symplectic automorphisms of K3 surfaces of arbitrary order

Cited by in corpus (1)

• Rational maps from punctual Hilbert schemes of K3 surfaces