On Smoothable Curve Singularities: Local Methods.
On special values for pencils of plane curve singularities.
On splitting up singularities of fundamental solutions to elliptic equations in ℂ2
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries.
On the approximate roots of polynomials
We give a simplified approach to the Abhyankar-Moh theory of approximate roots. Our considerations are based on properties of the intersection multiplicity of local curves.
On the bifurcation set of complex polynomial with isolated singularities at infinity
On the Bifurcation Variety of Some Non-Isolated Singularities.
On the conflict variety of an isolated hypersurface singularity.
On the ?-constant Stratum and the V-filtration: an Example.
On the diffeomorphic type of the complement to a line arrangement in a projective plane
We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011,...
On the discriminant of the Artin component
On the dual space of the Tjurina algebra attached to a semi-quasihomogeneous isolated singularity
A dual space of the Tjurina algebra attached to a non-quasihomogeneous unimodal or bimodal singularity is considered. It is shown that almost every algebraic local cohomology class, belonging to the dual space, can be characterized as a solution of a holonomic system of first order differential equations.
On the Euler characteristic of the links of a set determined by smooth definable functions
The purpose of this paper is to carry over to the o-minimal settings some results about the Euler characteristic of algebraic and analytic sets. Consider a polynomially bounded o-minimal structure on the field ℝ of reals. A () smooth definable function φ: U → ℝ on an open set U in ℝⁿ determines two closed subsets W := u ∈ U: φ(u) ≤ 0, Z := u ∈ U: φ(u) = 0. We shall investigate the links of the sets W and Z at the points u ∈ U, which are well defined up to a definable homeomorphism. It is proven...
On the Euler characteristic of the real Milnor fibres of an analytic function
The paper is concerned with the relations between real and complex topological invariants of germs of real-analytic functions. We give a formula for the Euler characteristic of the real Milnor fibres of a real-analytic germ in terms of the Milnor numbers of appropriate functions.
On the Existence of Analytic Contractions.
On the fiber of the compound of a real analytic function by a projection
Sia con una funzione analitica. Se il luogo critico di è compatto, esiste una fibrazione localmente triviale associata ai livelli . Supponiamo e sia la proiezione . Sotto una condizione sul luogo critico di esiste anche una fibrazione localmente triviale associata ai livelli di . Siano e le fibre rispettitive, e l'intervallo unità reale. Dimostriamo qui che è omeomorfa al prodotto . Nel caso di polinomi studiamo criteri effettivi. Diamo inoltre un'applicazione del risultato...
On the functoriality of stratified desingularizations.
On the Gauss-Manin Connection of an Isolated Hypersurface Singularity.
On the geometry of polynomial mappings at infinity
We associate to a given polynomial map from to itself with nonvanishing Jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.
On the height of foliated surfaces with vanishing Kodaira dimension.
We prove that the height of a foliated surface of Kodaira dimension zero belongs to (1, 2, 3, 4, 5, 6, 8, 10, 12). We also construct an explicit projective model. for Brunella's very special foliation.