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Quadratic forms and singularities of genus one or two
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 1, pp. 15-69.

On étudie les singularités obtenues en contractant le diviseur maximal des surfaces (non kählerienne) qui contiennent des coquilles sphériques globales. Ces singularités sont de genre 1 ou 2, peuvent être -Gorenstein, numériquement Gorenstein ou de Gorenstein. On définit une famille de polynômes qui dépendent de la configuration des courbes rationnelles pour calculer les discriminants des formes quadratiques associées à ces singularités. Un invariant topologique multiplicatif, défini à partir des arbres du graphe détermine le coefficient de torsion des 1-formes holomorphes tordues qui ne s’annulent pas sur le complémentaire du point singulier.

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 holomorphic 1-form on the complement of the singular point.

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DOI : https://doi.org/10.5802/afst.1285
@article{AFST_2011_6_20_1_15_0,
     author = {Georges Dloussky},
     title = {Quadratic forms and singularities of genus one or two},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {15--69},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 20},
     number = {1},
     year = {2011},
     doi = {10.5802/afst.1285},
     zbl = {pre05903978},
     mrnumber = {2829832},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1285/}
}
Georges Dloussky. Quadratic forms and singularities of genus one or two. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 1, pp. 15-69. doi : 10.5802/afst.1285. https://afst.centre-mersenne.org/articles/10.5802/afst.1285/

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