2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148438We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed.29 pages, LaTeX2e, General revision including error correctionsAlgebraic Geometrytext