Complement of Donaldson's symplectic submanifold

I am just starting to learn more symplectic geometry on Stein manifolds. I understand that an important class of Stein manifolds arises as the complement of a Donaldson's codimension two symplectic submanifold. I was wondering where I can find an actual proof of this important fact. Any comments or explanations will be more than welcome.

• Thank you very much for the posting. Can you fill in with more details? In the complex projective case, the complement of a hypersurface $V$ is stein because there is a pluri-harmonic function $\log \vert\vert s\vert\vert^2$, where $s$ is a holomorphic section which vanishes exactly at $V$. In the almost complex case, how can we proceed? Oct 25, 2013 at 15:36