Reduction of Singularities of Three-Dimensional Line Foliations

Details Reduction of Singularities of Three-Dimensional Line Foliations Reduction of Singularities of Three-Dimensional Line Foliations

2010-09-07

arxiv.org/abs/1009.1348v1

Mathematics

Algebraic Geometry

Scientific paper

We give a birational reduction of singularities for one dimensional foliations in ambient spaces of dimension three. To do this, we first prove the existence of a Local Uniformization in the sense of Zariski. The reduction of singularities is then obtained by a gluing procedure for Local Uniformization similar to Zariski's one, using an axiomatization of Zariski's work by Olivier Piltant.

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