Resolution of Irreducibles Quasi Ordinary Surfaces
DOI:
https://doi.org/10.17268/sel.mat.2018.02.09Keywords:
Quasi ordinary algebroid surfaces, resolution of singularities, blowups, quasi ordinary ringsAbstract
The aim of this work is to study and describe the resolution or desingularization of irreducible quasi ordinary surfaces, following Lipman’s approach ( [6], [7]).
To achieve our goal, we define the quasi ordinary surfaces and describe their parametrization by quasi ordinary branches, we also define the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, then we
study the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we define the special
transforms of a quasi ordinary ring and show that they are again quasi ordinary.
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