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Polyèdre de Newton et genre géométrique d’une singularité intersection complète. (French) Zbl 0564.32006
Let \(f_ 1,...,f_ k\) be polynomials in d complex variables, and let \(\Gamma^+_ 1,...,\Gamma^+_ k\) denote the corresponding Newton polyhedra. The author proves that the equations \(f_ 1=...=f_ k=0\) define an isolated complete intersection singularity at the origin if the coefficients of \(f_ 1,...,f_ k\) satisfy a suitable condition of non- degeneracy with respect to the system \((\Gamma^+_ 1,...,\Gamma^+_ k)\). The geometric genus of this singularity is calculated in terms of the elementary geometry of the system of polyhedra \((\Gamma^+_ 1,...,\Gamma^+_ k)\). The proofs use resolution of singularities via toroidal embeddings.
Reviewer: K.Wirthmüller

MSC:
32S05 Local complex singularities
14B05 Singularities in algebraic geometry
58C15 Implicit function theorems; global Newton methods on manifolds
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