2012/05/31 by Ingrid Bauer, Fabrizio Catanese, Bauer, Ingrid +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1205.7042
openalex publication_date 2012/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a family of minimal surfaces of general type with pg = 0,\nK2=7, constructed by Inoue in 1994, is indeed a connected component of the\nmoduli space: indeed that any surface which is homotopically equivalent to an\nInoue surface belongs to the Inoue family.\n The ideas used in order to show this result motivate us to give a new\ndefinition of varieties, which we propose to call Inoue-type manifolds: these\nare obtained as quotients \X / G, where \X is an ample divisor in a\nK(\Γ, 1) projective manifold Z, and G is a finite group acting freely on\n\X . For these type of manifolds we prove a similar theorem to the above,\neven if weaker, that manifolds homotopically equivalent to Inoue-type manifolds\nare again Inoue-type manifolds.\n