We show that every negative definite configuration of symplectic surfaces in a symplectic –manifold has a strongly symplectically convex neighborhood. We use this to show that if a negative definite configuration satisfies an additional negativity condition at each surface in the configuration and if the complex singularity with resolution diffeomorphic to a neighborhood of the configuration has a smoothing, then the configuration can be symplectically replaced by the smoothing of the singularity. This generalizes the symplectic rational blowdown procedure used in recent constructions of small exotic –manifolds.
"Symplectic surgeries and normal surface singularities." Algebr. Geom. Topol. 9 (4) 2203 - 2223, 2009. https://doi.org/10.2140/agt.2009.9.2203