Stein Domains in Complex Surfaces

Franc Forstneric

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Stein Domains in Complex Surfaces

Franc Forstneric

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Abstract

Let S be a closed connected real surface and f a smooth embedding or immersion of S into a complex surface X. Assuming that the number of complex points of the immersion (counted with algebraic multiplicities) is non-positive we prove that f can be uniformly approximated by an isotopic immersion g whose image g(S) in X has a basis of open Stein neighborhoods which are homotopy equivalent to g(S). We obtain precise results for surfaces in the complex projective plane CP^2 and find an immersed symplectic sphere in CP^2 with a Stein neighborhood. Conversely, the generalized adjunction inequality for embedded oriented real surfaces in complex surfaces shows that the existence of a Stein neighborhood implies non-positivity of the number of complex points.

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BibTeX RIS

Franc Forstneric. 2003-03-03. Stein Domains in Complex Surfaces. https://arxiv.org/abs/math/0201097

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