Considérons une variété régulière analytique M sur le corps réel ou complexe, un faisceau d'idéaux J défini sur M, un diviseur à croisement normaux simples E et une distribution singulière involutive Θ tangent à E.L'objectif principal de ce travail est d'obtenir une résolution des singularités du faisceau d'idéaux J qui préserve certaines ``bonnes" propriétés de la distribution singulière Θ. Plus précisément, la propriété de R-monomialité : l'existence d'intégrales premières monomiales. Ce problème est naturel dans le contexte où on doit étudier l'interaction d'une variété et d'un feuilletage et, donc, est aussi reliée au problème de la monomilisation des applications et de résolution ``quasi-lisse" des familles d'idéaux.- Le premier résultat donne une résolution globale si le faisceau d'idéaux J est invariant par la distribution singulière;- Le deuxième résultat donne une résolution globale si la distribution singulière Θ est de dimension 1 ;- Le troisième résultat donne une uniformisation locale si la distribution singulière Θ est de dimension 2.On présente aussi deux utilisations des résultats précédents. La première application concerne la résolution des singularités en famille analytique, soit pour une famille d'idéaux, soit pour une famille de champs de vecteurs. Pour la deuxième, on applique les résultats à un problème de système dynamique, motivé par une question de Mattei. / Let M be an analytic manifold over the real or complex field, J be a coherent and everywhere non-zero ideal sheaf over M, E be a reduced SNC divisor and Θ an involutive singular distribution everywhere tangent to E. The main objective of this work is to obtain a resolution of singularities for the ideal sheaf J that preserves some ``good" properties of the singular distribution Θ. More precisely, the R-monomial property : the existence of local monomial first integrals. This problem arises naturally when we study the ``interaction" between a variety and a foliation and, thus, is also related with the problem of monomialization of maps and of ``quasi-smooth" resolution of families of ideal sheaves.- The first result is a global resolution if the ideal sheaf J is invariant by the singular distribution Θ;- The second result is a global resolution if the the singular distribution Θ has leaf dimension 1;- The third result is a local uniformization if the the singular distribution Θ has leaf dimension 2;We also present two applications of the previous results. The first application concerns the resolution of singularities in families, either of ideal sheaves or vector fields. For the second application, we apply the results to a dynamical system problem motivated by a question of Mattei.

Let M be an analytic manifold over the real or complex field, J be a coherent and everywhere non-zero ideal sheaf over M, E be a reduced SNC divisor and Θ an involutive singular distribution everywhere tangent to E. The main objective of this work is to obtain a resolution of singularities for the ideal sheaf J that preserves some ''good" properties of the singular distribution Θ. More precisely, the R-monomial property : the existence of local monomial first integrals. This problem arises naturally when we study the ''interaction" between a variety and a foliation and, thus, is also related with the problem of monomialization of maps and of ''quasi-smooth" resolution of families of ideal sheaves.- The first result is a global resolution if the ideal sheaf J is invariant by the singular distribution Θ;- The second result is a global resolution if the the singular distribution Θ has leaf dimension 1;- The third result is a local uniformization if the the singular distribution Θ has leaf dimension 2;We also present two applications of the previous results. The first application concerns the resolution of singularities in families, either of ideal sheaves or vector fields. For the second application, we apply the results to a dynamical system problem motivated by a question of Mattei.

Made available in DSpace on 2016-12-23T14:34:49Z (GMT). No. of bitstreams: 1 Carla Rodrigues Almeida.pdf: 592195 bytes, checksum: 070fca888db010e772db2fafedfd378d (MD5) Previous issue date: 2012-08-13 / O objetivo deste trabalho é estudar as folheações que surgem a partir de estruturas de Nambu e apresentar a relação entre formas diferenciais e algumas destas estruturas. Mais precisamente, fazer um estudo da geometria de Poisson e de folheações singulares, enfatizando o caso da folheação simplética que surge da estrutura de Poisson e, em seguida, apresentar a geometria de Nambu, estudando o caso das folheações que surgem destas estruturas de ordem maiores ou iguais a três. Neste caso particular, vamos mostrar como tais estruturas de Nambu se relacionam com formas diferenciais e, por esta relação, classificar as estruturas de Nambu lineares através de um resultado de classificação de p-formas integráveis / The aim of this work is to study the foliations that arise from Nambu structures and present the relationship between differential forms and some of this structures. More specifically, to make a study of the Poisson geometry and of singular foliations, emphasiz-ing the case of the simplectic foliation that arises from the Poisson structure and then, to present the Nambu geometry, studying the case of the foliations that arise from the this structures of order grater than or equal to three. In this particular case, we shall show how this Nambu structures are related with differential formas and, by this relationship, classify linear Nambu structure through a result of classification of integrable differential p-forms