On analytic sets and functions with given isolated singularities.
On classification of real singularities.
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.
On Halphen’s Theorem and some generalizations
Let be a germ at of an irreducible analytic set of dimension , where and is a singular point of . We study the question: when does there exist a germ of holomorphic map such that ? We prove essentialy three results. In Theorem 1 we consider the case where is a quasi-homogeneous complete intersection of polynomials , that is there exists a linear holomorphic vector field on , with eigenvalues such that , where is a matrix with entries in . We prove that if there exists...
On hypersurface singularities which are stems
On Isolated Gorenstein Singularities.
On polar invariants of hypersurface singularities
On p-parameter bifurcation of an n-dimensional function-germ.
On Right-Equivalence.
On simple fibered knots in S5 and the existence of decomposable algebraic 3-knots.
On simple germs with non-isolated singularities.
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 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 Gauss-Manin Connection of an Isolated Hypersurface Singularity.
On the Łojasiewicz exponent for analytic curves
An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.
On the Łojasiewicz exponent near the fibre of polynomial mappings
We give the formula expressing the Łojasiewicz exponent near the fibre of polynomial mappings in two variables in terms of the Puiseux expansions at infinity of the fibre.
On the Łojasiewicz exponent of the gradient of a holomorphic function
The Łojasiewicz exponent of the gradient of a convergent power series h(X,Y) with complex coefficients is the greatest lower bound of the set of λ > 0 such that the inequality holds near for a certain c > 0. In the paper, we give an estimate of the Łojasiewicz exponent of grad h using information from the Newton diagram of h. We obtain the exact value of the exponent for non-degenerate series.
On the Mixed Hodge Structure on the Cohomology of the Milnor Fibre.
On the Monodromy Theorem for Isolated Hypersurface Singularities.