Generalized Burniat type surfaces are etale quotients of a hypersurface of multidegree (2,2,2) inside a product of three elliptic curves by (Z/2Z)^3. These surfaces are generalizations of a construction of Burniat surfaces given by Inoue and they have invariants K^2 = 6, chi = 1. These surfaces were completely classified and their moduli spaces were determined in a joint paper with F. Catanese and D. Frapporti.

In the case p_g=0 Bloch's conjecture for rational equivalence classes of zero cycles can be verified (cf. B.-Frapporti).

If a generalized Burniat type surface S is defined over the rational numbers, then the set of rational points of S, outside a finite number of elliptic curves, is finite. In a joint paper with M. Stoll this has been made explicit for classical Burniat surfaces.