2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107548Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles moduli spaces over X. We give examples for one marked point showing that the Poincare polynomials depend on the system of weights of the parabolic bundle.Typos corrected, better explanations for formula in (6)Algebraic Geometry14D20, 14H60text