Function germs defined on isolated hypersurface singularities
Germs of holomorphic vector fields in C3 without a separatrix.
Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities.
Hamiltonian stability and subanalytic geometry
In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function which is real analytic around a...
Hermitian (a,b)-modules and Saito's "higher residue pairings"
Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible, and we give...
Holomorphic bijections of algebraic sets
We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].
Holomorphic functions with singularities on algebraic sets.
Identité de Bernstein pour une fonction homogène à singularité isolée
Improper intersection of analytic curves.
Infinitesimal Deformations of Cusp Singularities.
Integral closure of modules and Whitney equisingularity.
Invariants of bi-Lipschitz equivalence of real analytic functions
We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (ℝ,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x| |grad f(x)| is comparable to the size of |f(x)|.
Invariants of equidimensional maps
To a given complex-analytic equidimensional corank-1 germ f, one can associate a set of integer 𝓐-invariants such that f is 𝓐-finite if and only if all these invariants are finite. An analogous result holds for corank-1 germs for which the source dimension is smaller than the target dimension.
Isolated critical points of mappings from R4 to R2 and a natural splitting of the Milnor number of a classical fibered link. Part I: Basic theory; examples.
Killing divisor classes by algebraisation
It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.
Kodaira singularities and an extension of Arnold's strange duality
L2-cohomology and intersection homology of certain algebraic varieties with isolated singularities.
La construction de la déformation semi-universelle d'un germe de variété analytique complexe
La forme hermitienne canonique sur la partie invariante de la cohomologie de la fibre de Milnor d'une singularité isolée de polynôme quasi-homogène
Le calcul de la forme hermitienne canonique pour un polynome homogène à singularité isolée.