Sur les exposants de Lojasiewicz.
Sur l'existence d'intégrales premières holomorphes
Sur l'homologie des courants à support dans un ensemble semi-analytique
Sur l'idéal jacobien d'une courbe plane
Sur l'image d'un morphisme analytique réel propre
Sur l'irréductibilité dans l'anneau des séries de Dirichlet analytiques.
We discuss some local analytic properties of the ring of Dirichlet series. We obtain mainly the equivalence between the irreducibility in the analytic ring and in the formal one. In the same way we prove that the ring of analytic Dirichlet series is integrally closed in the ring of formal Dirichlet series. Finally we introduce the notion of standard basis in these rings and we give a finitely generated ideal which does not admit standard bases.
Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique
Sur un point de la théorie des fonctions algébriques de deux variables
Tangencies of generic real projective hypersurfaces.
Tangentes limites, cône de Whitney et régularité par intersection
Nous caractérisons, en terme de dimension (topologique et de Hausdorff) des fibres des espaces de limites de tangents et du cône de Whitney, les conditions de régularité et sur une stratification . Nous précisons ces résultats lorsque les espaces qui interviennent ne sont pas fractals, en particulier lorsque la stratification est sous-analytique.
Tempered solutions of -modules on complex curves and formal invariants
Let be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of -modules on induces a fully faithful functor on a subcategory of germs of formal holonomic -modules. Further, given a germ of holonomic -module, we obtain some results linking the subanalytic sheaf of tempered solutions of and the classical formal and analytic invariants of .
The Briançon-Skoda number of analytic irreducible planar curves
The Briançon-Skoda number of a ring is defined as the smallest integer k, such that for any ideal and , the integral closure of is contained in . We compute the Briançon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.
The cancellation property for direct products of analytic space germs.
The classification of curvilinear angles in the complex plane and the groups of holomorphic diffeomorphisms
The degree at infinity of the gradient of a polynomial in two real variables
Let f:ℝ² → ℝ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient ∇f in terms of the real branches at infinity of the level curves {f(x,y) = λ} for some λ ∈ ℝ. The formula obtained is a counterpart at infinity of the local formula due to Arnold.
The directional dimension of subanalytic sets is invariant under bi-Lipschitz homeomorphisms
Let be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at .Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and are also subanalytic. In particular if two subanalytic...
The finiteness of compact varieties in
The Formal Hodge Filtration.
The Gleason problem for , , .
The Hartogs-type extension theorem for meromorphic mappings into -complete complex spaces
Si dimostra un risultato di prolungamento per applicazioni meromorfe a valori in uno spazio -completo che generalizza direttamente il risultato classico di Hartogs e migliora risultati di K. Stein.