Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces

Abstract

This is the first in a series of articles on the moduli spaces of Burniat surfaces. We prove that Burniat surfaces are Inoue surfaces and we calculate their fundamental groups. As a main result of this paper we prove that every smooth projective surface which is homotopically equivalent to a primary Burniat surface (i.e., a Burniat surface with K^2 = 6) is indeed a primary Burniat surface.

References in corpus (1)

• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups

Cited by in corpus (5)

• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups
• Generalized Burniat type surfaces and Bagnera-de Franchis varieties
• Symplectic generic complex structures on 4-manifolds with b_+ = 1
• Burniat-type surfaces and a new family of surfaces with p_g = 0, K^2 = 3
• Bloch's conjecture for Generalized Burniat Type surfaces with $p_g=0$