An essentially saturated surface not of Kaehler-type

Details An essentially saturated surface not of Kaehler-type An essentially saturated surface not of Kaehler-type

2007-12-19

arxiv.org/abs/0712.3234v1

Mathematics

Complex Variables

10 pages

Scientific paper

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 compact
complex surfaces without curves, it is shown that these are the only examples.

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