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

2009/09/21 by Ingrid Bauer, Fabrizio Catanese, Bauer, Ingrid +1
Mathematics · #14D22 #14H30 #14J10 #14J25 #14J29 #20F34 #32G05 #32Q30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14D22 #msc:14H30 #msc:14J10 #msc:14J25 #msc:14J29 #msc:20F34 #msc:32G05 #msc:32Q30

paper · pdf · doi:10.48550/arxiv.0909.3699

arxiv created 2009/09/21 · openalex publication_date 2009/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 K² = 6) is indeed a primary Burniat surface.

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