Stein Domains in Complex Surfaces

Details Stein Domains in Complex Surfaces Stein Domains in Complex Surfaces

2002-01-11

arxiv.org/abs/math/0201097v3

J. Geom. Anal., 13 (2003), 77-94

Mathematics

Complex Variables

Journal of Geometric Analysis, to appear

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Stein Domains in Complex Surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stein Domains in Complex Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stein Domains in Complex Surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-279340