Inoue type manifolds and Inoue surfaces: a connected component of the moduli space of surfaces with
Ingrid Bauer
Universität Bayreuth, GermanyFabrizio Catanese
Universität Bayreuth, Germany
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Abstract
We show that a family of minimal surfaces of general type with , 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 , where is an ample divisor in a projective manifold , and is a finite group acting freely on . 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.