Bloch's conjecture for Generalized Burniat Type surfaces with $p_g=0$

TL;DR

This paper proves Bloch's conjecture for regular generalized Burniat type surfaces with geometric genus zero, demonstrating that their zero cycles are rationally equivalent to zero using automorphism techniques.

Contribution

It introduces a simplified automorphism method to establish Bloch's conjecture for a new class of surfaces with p_g=0.

Findings

Bloch's conjecture holds for regular generalized Burniat type surfaces.

Automorphism techniques effectively prove triviality of zero cycles.

Method simplifies previous approaches to similar problems.

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 0 is trivial for surfaces with geometric genus zero, for regular generalized Burniat type surfaces. The technique is the method of "enough automorphisms" introduced by Inose-Mizukami in a simplified version due to the first author.