2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62651We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements reduces the problem to studying certain triangulated spaces $X_{λ,μ}$. We present a combinatorial description of the cell structure of $X_{λ,μ}$ using the language of marked forests. As applications we obtain a new proof of a theorem of Arnold and a counterexample to a conjecture of Sundaram and Welker, along with a few other smaller results.CombinatoricsAlgebraic Topology32S20; 05E15, 32S60, 58K15text