Quadratic forms and singularities of genus one or two

Details Quadratic forms and singularities of genus one or two Quadratic forms and singularities of genus one or two

2007-02-15

arxiv.org/abs/math/0702467v2

Mathematics

Complex Variables

40 pages, 33 figures, misprints corrected, section 3.4 added

Scientific paper

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 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.

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