Non-smoothable varieties.
Normal cones and sheaves of relative jets
Normal surface singularities admitting contracting automorphisms
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.
Normalization theorems for certain modular discriminantal loci
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...
Offenheit der Versalität in der analytischen Geoemtrie.
On analytic sets and functions with given isolated singularities.
On arc-analytic functions definable by a Weierstrass system
This paper presents certain characterizations through blowing up of arc-analytic functions definable by a convergent Weierstrass system closed under complexification.
On associated discriminants for polynomials in one variable.
On asymptotic critical values and the Rabier Theorem
Let X ⊂ kⁿ be a smooth affine variety of dimension n-r and let be a polynomial dominant mapping. It is well-known that the mapping f is a locally trivial fibration outside a small closed set B(f). It can be proved (using a general Fibration Theorem of Rabier) that the set B(f) is contained in the set K(f) of generalized critical values of f. In this note we study the Rabier function. We give a few equivalent expressions for this function, in particular we compare this function with the Kuo function...
On b-function, spectrum and rational singularity.
On blowing up versal discriminants
It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of and singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain deformations...
On Bochner-Martinelli residue currents and their annihilator ideals
We study the residue current of Bochner-Martinelli type associated with a tuple of holomorphic germs at , whose common zero set equals the origin. Our main results are a geometric description of in terms of the Rees valuations associated with the ideal generated by and a characterization of when the annihilator ideal of equals .
On classification of real singularities.
On condition of a stratified mapping
For a stratified mapping , we consider the condition concerning the kernel of the differential of . We show that the condition is equivalent to the condition which has a more obvious geometric content.
On deformations of monomial curves
On Equisingular Deformations of Cone-Like Surface Singularities.
On Fatou-Julia decompositions
We propose a Fatou-Julia decomposition for holomorphic pseudosemigroups. It will be shown that the limit sets of finitely generated Kleinian groups, the Julia sets of mapping iterations and Julia sets of complex codimension-one regular foliations can be seen as particular cases of the decomposition. The decomposition is applied in order to introduce a Fatou-Julia decomposition for singular holomorphic foliations. In the well-studied cases, the decomposition behaves as expected.
On geometry of fronts in wave propagations
We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
On gradient at infinity of semialgebraic functions
Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number such that |x|·|∇f| and are separated at infinity. If c is a regular value and , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.