2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198834We construct topological recursion relations (TRR's) at higher genera $g\ge2$ for general 2-dimensional topological field theories coupled to gravity. These TRR's when combined with Virasoro conditions enable one to determine the number of higher genus holomorphic curves in any Fano varieties. In the case of $CP^2$ we reproduce the known results at genus $g=2$.Latex, 8 pages, the instanton numbers of $CP^2$ at genus 3 added, the version to appear in Adv.Theor.Math.PhysHigh Energy Physics - TheoryAlgebraic Geometrytext