2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145360We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminant of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting of a non-vanishing holomorphic 1-form on the complement of the singular point.40 pages, 33 figures, misprints corrected, section 3.4 addedComplex VariablesAlgebraic Geometry32S25; 32J15; 14J17; 14B05; 11C20; 15A36text