Intersection theory in complex analytic geometry
We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
Intersections of analytic sets with linear subspaces
Intertwined mappings
Invariants polaires de courbes planes.
Isolated intersection multiplicity and regular separation of analytic sets
An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.
Lieu discriminant d’un germe analytique de corang 1 de vers
On considère des germes d’applications analytiques de vers , de corang 1, finis, à lieu critique irréductible. De corang 1 signifie qu’il s’écrit après un bon choix de coordonnées locales sous la forme: où . On donne des conditions nécessaires et suffisantes pour qu’une courbe plane irréductible soit le lieu discriminant d’un tel germe d’applications : ce sont des conditions numériques portant sur les exposants de Puiseux. Ce problème est lié à celui de la représentation d’une variété lagrangienne...
Linear Complementary Inequalities for Orders of Germs of Analytic Functions.
Local algebraicity of analytic sets.
Local generalizations of Lefschetz-Zariski theorems.
Monodromy of functions defined on isolated singularities of complete intersections
Normalisation des champs de vecteurs holomorphes
Note on the degree of Cº-sufficiency of plane curves.
Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the...
Nullstellensatz and cycles of zeroes of holomorphic mappings
The local Nullstellensatz exponent for holomorphic mappings via intersection theory for the cases of isolated and quasi-complete intersection is considered.
On analytic sets and functions with given isolated singularities.
On hypersurface singularities which are stems
On improper isolated intersection in complex analytic geometry
On microlocal -function
On simple germs with non-isolated singularities.
On the division of functions of class by real analytic functions
On the finiteness of Pythagoras numbers of real meromorphic functions
We consider the 17th Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real meromorphic functions. We deduce that an affirmative solution to the 17th Hilbert Problem for global real analytic functions implies the finiteness of the Pythagoras number of the field of global real meromorphic functions, hence that of the field of real...