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Quasi-homogeneous blowing-ups. (Éclatements quasi homogènes.) (French) Zbl 0861.32021
The author considers smooth germs of the plane whose singularities are algebraically isolated. She defines an algorithm of desingularization using quasi-homogeneity. To each germ it is associated a Newton polygon which allows to choose quasi-homogeneity type at each step of the algorithm. The number of blowing-ups can be bounded from above using the Newton polygon. The number of elementary operations, blowing-ups or change of coordinates can be bounded by a function of the codimension of the germ.

MSC:
32S25 Complex surface and hypersurface singularities
32S45 Modifications; resolution of singularities (complex-analytic aspects)
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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