  The main goal of this paper is to give constructive proofs of several
existence results for symplectic embeddings. The strong relation between
symplectic packings and singular symplectic curves, which can be derived from
McDuff's inflations on the blow-ups, is revisited through a new inflation
technique that lives at the level of the manifold. As an application, we
explain constructions of maximal symplectic packings of $P^2$ by 6, 7 or 8
balls.
