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Singularités quasi-ordinaires toriques et polyèdre de Newton du discriminant

  • P. D. González Pérez (a1)

Abstract

Nous étudions les polynômes $F\,\in \,\mathbb{C}\,\{{{S}_{\mathcal{T}}}\}\,\left[ Y \right]$ à coefficients dans l’anneau de germes de fonctions holomorphes au point spécial d’une variété torique affine. Nous généralisons à ce cas la paramétrisation classique des singularités quasi-ordinaires. Cela fait intervenir d’une part une généralization de l’algorithme de Newton-Puiseux, et d’autre part une relation entre le polyèdre de Newton du discriminant de $F$ par rapport à $Y$ et celui de $F$ au moyen du polytope-fibre de Billera et Sturmfels. Cela nous permet enfin de calculer, sous des hypothèses de non dégénérescence, les sommets du polyèdre de Newton du discriminant a partir de celui de $F$ , et les coefficients correspondants à partir des coefficients des exposants de $F$ qui sont dans les arêtes de son polyèdre de Newton.

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References

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