Miguel Fernández Duque – Local uniformization of codimension one foliations

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Date(s) - 18 octobre 2018

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In 1940 O. Zariski obtained Local Uniformization on algebraic varieties. Using this result, which is true in arbitrary dimension, in 1944 he obtained Resolution of Singularities in dimension three. It was twenty years later, in 1964, when H. Hironaka published his celebrated paper obtaining Resolution of Singularities in any dimension. In the case of codimension one foliations, we only know reduction of singularities results in lower dimensions. In fact, only in dimension two (A. Seidenberg 1968) and three (F. Cano 2004). Following the ideas of Zariski, in this talk we present the result of Local Uniformization for codimension one foliations defined in ambient spaces of arbitrary dimension. This is a joint work with F. Cano.[