Inoue type manifolds and Inoue surfaces: a connected component of the moduli space of surfaces with K2=7,pg=0K^2=7, p_g = 0

  • Ingrid Bauer

    Universität Bayreuth, Germany
  • Fabrizio Catanese

    Universität Bayreuth, Germany
Inoue type manifolds and Inoue surfaces: a connected component of the moduli space of surfaces with $K^2=7, p_g = 0$ cover
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Abstract

We show that a family of minimal surfaces of general type with pg=0,K2=7p_g = 0, K^2=7, constructed by Inoue in 1994, is indeed a connected component of the moduli space: indeed that any surface which is homotopically equivalent to an Inoue surface belongs to the Inoue family.

The ideas used in order to show this result motivate us to give a new definition of varieties, which we propose to call Inoue type manifolds: these are obtained as quotients X^/G\hat{X} / G, where X^\hat{X} is an ample divisor in a K(Γ,1)K(\Gamma, 1) projective manifold ZZ, and GG is a finite group acting freely on X^\hat{X} . For these types of manifolds we prove a similar theorem to the above, even if weaker, that manifolds homotopically equivalent to Inoue type manifolds are again Inoue type manifolds.