Submission date: 21 December 2007

Abstract:

It is shown that if X is an Inoue surface of type S_M then the irreducible components of the Douady space of X^n are compact, for all n>0. This gives an example of an essentially saturated compact complex manifold (in the sense of model theory) that is not of Kaehler-type. Among the known strongly minimal compact complex surfaces, it is shown that these are the only examples.

Mathematics Subject Classification: 32J15; 03C98

Keywords and phrases: compact complex manifold, Inoue surface, essential saturation

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