Fibered neighborhoods of curves in surfaces
Let \(M\) a smooth two-dimensional complex manifold and \(S \subset X\) a smooth compact Riemann surface of genus \(g\). Here the authors prove that if the normal bundle \(N_S\) of \(S\) in \(M\) has degree \(S\cdot S \leq 3-2g\), then a small neighborhood of \(S\) in \(M\) is fibered equivalent (and in particular biholomorphic) to a neighborhood of \(S\) in \(N_S\). For a very good introduction and many interesting results in the higher dimensional case, see the e-print [\textit{C. Camacho} and \textit{H. Movasati}, Neighborhoods of analytic varieties in complex manifolds, arXiv: math.CV/0208058].
holomorphically convex neighborhood of curves
scientific article; zbMATH DE number 2013175