Let k be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the Łojasiewicz exponent £ (a) of ...

We prove that if two plane curve singularities are equisingular, then they are topologically equivalent. The method we will use is P. Fortuny Ayuso’s who proved this result for irreducible plane curve singularities.

We prove that in order to find the value of the Łojasiewicz exponent ł(f) of a Kouchnirenko non-degenerate holomorphic function f : (Cn; 0) → (C; 0) with an isolated singular point at the origin, it is enough to find this ...

Let K be an algebraically closed field of characteristic 0 and let ƒ ϵ K[[X]] [Y] be monic. Using the properties of approximate roots given in [J. Algebra 343 (2011), pp. 143-159] we propose some necessary conditions for ...

Let K be an algebraically closed field and let K((XQ)) denote the field of generalized series with coefficients in K. We propose definitions of the local Łojasiewicz exponent of F = ( f1, . . . , fm) ∈ K[[X, Y ]]m as ...

Podajemy nowy, elementarny dowód hipotezy o krotności Zariskiego w μ-constant rodzinach niezdegenerowanych osobliwości.