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

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

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.

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