Quasi-homogeneous blowing-ups (Q1814966)

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.