  Suppose that $C=(C_1,..., C_m)$ is a configuration of 2-dimensional
symplectic submanifolds in a symplectic 4-manifold $(X,\omega)$ with connected,
negative definite intersection graph $\Gamma_C$. We show that by replacing an
appropriate neighborhood of $\cup C_i$ with a smoothing $W_S$ of a normal
surface singularity $(S, 0)$ with resolution graph $\Gamma_C$, the resulting
4-manifold admits a symplectic structure. This operation generalizes the
rational blow-down operation of Fintushel-Stern for other configurations, and
therefore extends Symington's result about symplectic rational blow-downs.

Geometric Topology;Algebraic Geometry;Symplectic Geometry