2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59395Let G be a complex reductive group and let C be a smooth curve of genus at least one. We prove a converse to a theorem of Atiyah-Bott concerning the stratification of the space of holomorphic G-bundles on C. In case the genus of C is one, we establish that one has a stratification in the strong sense. The paper concludes with a characterization of the minimally unstable strata in case G is simple.Latex file, 34 pages, 5 figuresAlgebraic Geometrytext