Enumerative vs.\ symplectic invariants and obstruction bundles

We describe in detail a gluing construction for pseudoholo- morphic maps in symplectic geometry, including in the pres- ence of an obstruction bundle. The main motivation is to try to compare the symplectic and enumerative invariants of algebraic manifolds. These descriptions can also be used to enumerate rational curves with high-order degeneracies of lo- cal nature in projective spaces.