2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69681By using superisolated surface singularities whose link is a rational homology sphere we give counterexamples to some of the most important conjetures concernig invariants of normal surface singularities.Revised version, to appear in Journal of Algebraic GeometryAlgebraic GeometryCommutative Algebra14B05,14J17,32S25,57M27,57R57text