Factoriality of a ring of holomorphic functions
Familles de courbes sur les germes d'espaces analytiques
Fields with analytic structure
Filtration par le poids et monodromie entière
Finite morphisms between differentiable algebras.
Finiteness of semialgebraic types of polynomial functions.
Finiteness property for generalized abelian integrals
We study the integrals of real functions which are finite compositions of globally subanalytic maps and real power functions. These functions have finiteness properties very similar to those of subanalytic functions. Our aim is to investigate how such finiteness properties can remain when taking the integrals of such functions. The main result is that for almost all power maps arising in a -function, its integration leads to a non-oscillating function. This can be seen as a generalization of Varchenko...
Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Flatness testing over singular bases
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
Fonctions et feuilletages Levi-Flat. Étude locale
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
Formal relations between quasianalytic functions of some fixed class
In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides...
Forme hermitienne canonique sur la cohomologie de la fibre de Milnor d'une hypersurface à singularité isolée.
Formelle Standardmodelle hyperelliptischer Kurven.
Frobenius' theorem for differential forms on analytic spaces
Frontière d'une hypersurface pfaffienne et géométrie sous-analytique
Nous donnons une nouvelle démonstration d'un théorème de Cano-Lion-Moussu: la frontière d'une hypersurface pfaffienne non spiralante est une réunion localement finie de sous-variétés analytiques connexes.
Function germs defined on isolated hypersurface singularities