Cross theorems with singularities

Mathematics – Complex Variables

Scientific paper

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30 pages. A previous version is available at the ICTP preprints website (ref. IC2007073)

Scientific paper

We establish extension theorems for separately holomorphic mappings defined
on sets of the form W\setminus M with values in a complex analytic space which
possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary
complex manifolds and M is a set of singularities which is locally pluripolar
(resp. thin) in fibers.

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