# Generalized Burniat type surfaces

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Ingrid Bauer

created by risa on 16 Oct 2015

23 oct 2015
-- 14:30

Aula Dal Passo, Dip. Matematica, Università "Tor Vergata", Roma

**Abstract.**

Generalized Burniat type surfaces are etale quotients of a hypersurface of (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.