Deformations of Stein structures and extensions of holomorphic mappings

Details Deformations of Stein structures and extensions of holomorphic mappings Deformations of Stein structures and extensions of holomorphic mappings

2005-09-19

arxiv.org/abs/math/0509419v2

Math. Res. Lett. 14 (2007), 343--357

Mathematics

Complex Variables

To appear in Math. Res. Lett

Scientific paper

Let X be a Stein manifold, A a closed complex subvariety of X, and f a continuous map from X to a complex manifold Y whose restriction to A is holomorphic. After a homotopic deformation of the Stein structure outside a neighborhood of A in X (and of its smooth structure when X is a Stein surface)we find a holomorphic map from X to Y which agrees with f on A and which is homotopic to f relative to A. The analogous results in the case when the variety A is empty have been obtained in the preprint math.CV/0507212.

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