Quadratic forms and singularities of genus one or two

Georges Dloussky (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We 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 compute the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant

Mots clés: singularities; Gorenstein; complex surface

Domaines: Variables complexes [math.CV]

Georges Dloussky. Quadratic forms and singularities of genus one or two. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2011, 20, pp.15-69. ⟨hal-00143289⟩