2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150193We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's formula for rational plane curves of given degree.77 pages, Tex type: AMSLaTex in LaTex 2.09 compatibility mode, figures are not included in the package, for a copy with pictures write to bwatson@abel.harvard.eduAlgebraic Geometrytext