2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60045The article investigates the following question: given a projective variety X acted on by a connected and reductive group G, which is the relationship between the Gromov-Witten invariants of X and those of X//G? In this study we shall also try to give an algebraic approach to the so called Hamiltonian Gromov-Witten invariants which have appeared rather recenly in the literature.revised version, 37 pages, LaTeXAlgebraic Geometry14H10, 14L30text