We present a new method to prove transversality for holomorphic curves in symplectic manifolds, and show how it leads to a definition of genus zero Gromov-Witten invariants. The main idea is to introduce additional marked points that are mapped to a symplectic hypersurface of high degree in order to stabilize the domains of holomorphic maps.
"Symplectic hypersurfaces and transversality in Gromov-Witten theory." J. Symplectic Geom. 5 (3) 281 - 356, September 2007.