Quadratic forms and singularities of genus one or two

2007/02/15 by Georges Dloussky, Dloussky, Georges
Mathematics · #11C20 #14B05 #14J17 #15A36 #32J15 #32S25 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:11C20 #msc:14B05 #msc:14J17 #msc:15A36 #msc:32J15 #msc:32S25

paper · pdf · doi:10.48550/arxiv.math/0702467

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

arxiv created 2008/01/07 · arxiv updated 2009/12/01

Abstract

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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