| We consider a natural generalization of the symplectic sum, that is closely related to desingularization in algebraic geometry. We prove that the resulting generalized sum is diffeomorphic to the usual sum after performing certain symplectic blow-ups. Furthermore, we prove that the blow-ups can be performed in either summand without changing the result of the sum, partially generalizing results of Dusa McDuff and Margaret Symington.; In order to derive formulae for the Gromov-Witten invariants of such constructions, we need to consider how stable maps relative to V behave as V degenerates to a singular V 0. We define a notion of stable maps relative to a V 0 consisting of finitely many smooth components intersecting transversally, following the approach of Eleny Ionel and Thomas Parker. We prove that the moduli space of such maps is a smooth, compact orbifold. We also briefly investigate the relationship between maps relative to V 0 and those relative to a desingularization V. |
