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.