Bloch's conjecture for Inoue surfaces with p_g=0, K^2 =7

TL;DR

This paper proves Bloch's conjecture for a specific class of Inoue surfaces with p_g=0 and K^2=7, using automorphism methods related to their bidouble cover structure.

Contribution

It establishes Bloch's conjecture for Inoue surfaces with p_g=0, K^2=7, a case previously unverified, by applying the 'enough automorphisms' technique.

Findings

Bloch's conjecture holds for these Inoue surfaces.

The surfaces are described as bidouble covers of a nodal cubic.

Automorphism methods are effective in this proof.

Abstract

The aim of this article is to prove Bloch's conjecture (asserting that the group of rational equivalence classes of zero cycles of degree zero is trivial) for Inoue surfaces with p_g=0 and K^2 = 7. These surfaces can also be described as bidouble covers of the four nodal cubic, which allows to use the method of "enough automorphisms" introduced by Inose-Mizukami (in a simplified version).