The lattices and Möbius functions of stable closed subrootsystems and Hyperplane complements for classical Weyl Groups.
The Lê varieties, I.
The Le varieties, II.
The Le-Ramanujam Problem for Hypersurfaces with One-Dimensional Singular Sets.
The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero
The Łojasiewicz gradient inequality in a neighbourhood of the fibre
Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
The Łojasiewicz numbers and plane curve singularities
For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².
The Milnor fiber and the zeta function of the singularities of type
The Milnor Number and Deformations of Complex Curve Singularities.
The Milnor number of functions on singular hypersurfaces
The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical...
The monodromy conjecture for zeta functions associated to ideals in dimension two
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an...
The Monodromy Groups of Critical Points of Functions II.
The monodromy of a series of hypersurface singularities.
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
The number of critical points of a product of powers of linear functions.
The rational homotopy of Thom spaces and the smoothing of isolated singularities
Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question...
The real Seifert form and the spectral pairs of isolated hypersurface singularities
The Seiberg–Witten invariants of negative definite plumbed 3-manifolds
Assume that is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...
The Signature of Milnor Fibres and Duality Theorem for Strongly Pseudoconvex Manifolds.
The Signature of Smoothings of Complex Surface Singularities.