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On the Kähler Rank of Compact Complex Surfaces

Matei Toma (2008)

Bulletin de la Société Mathématique de France

Harvey and Lawson introduced the Kähler rank and computed it in connection to the cone of positive exact currents of bidimension ( 1 , 1 ) for many classes of compact complex surfaces. In this paper we extend these computations to the only further known class of surfaces not considered by them, that of Kato surfaces. Our main tool is the reduction to the dynamics of associated holomorphic contractions ( 2 , 0 ) ( 2 , 0 ) .

Quadratic forms and singularities of genus one or two

Georges Dloussky (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...

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