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.
@article{AFST_2011_6_20_1_15_0, author = {Dloussky, Georges}, 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, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 20}, number = {1}, year = {2011}, doi = {10.5802/afst.1285}, mrnumber = {2829832}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1285/} }
TY - JOUR AU - Dloussky, Georges TI - Quadratic forms and singularities of genus one or two JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 15 EP - 69 VL - 20 IS - 1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1285/ DO - 10.5802/afst.1285 LA - en ID - AFST_2011_6_20_1_15_0 ER -
%0 Journal Article %A Dloussky, Georges %T Quadratic forms and singularities of genus one or two %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 15-69 %V 20 %N 1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1285/ %R 10.5802/afst.1285 %G en %F AFST_2011_6_20_1_15_0
Dloussky, Georges. 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. http://archive.numdam.org/articles/10.5802/afst.1285/
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