A motivic study of generalized Burniat surfaces

Abstract

Generalized Burniat surfaces are surfaces of general type with $p_g=q$ and Euler number $e=6$ obtained by a variant of Inoue's construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer, Catanese and Frapporti. This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.