  In this paper, we investigate a relation between rational blowdown surgery
and minimal symplectic fillings of a given Seifert 3-manifold with a canonical
contact structure. Consequently, we determine a necessary and sufficient
condition for a minimal symplectic filling of a Seifert 3-manifold satisfying
certain conditions to be obtained by a sequence of rational blowdowns from the
minimal resolution of the corresponding weighted homogeneous surface
singularity. Furthermore, as an application of the main results, we prove that
every minimal symplectic filling of a large family of Seifert 3-manifolds with
a canonical contact structure is in fact realized as a Milnor fiber of the
corresponding weighted homogeneous surface singularity in the Appendix.
