5 papers · 1 filter
The Łojasiewicz exponent in non-degenerate deformations of surface singularities
Szymon Brzostowski, Tadeusz Krasiński, Grzegorz Oleksik
We prove the constancy of the Łojasiewicz exponent in non-degenerate -constant deformations of surface singularities. This is a positive answer to a question posed by B. Teissie…
The Łojasiewicz exponent of non-degenerate surface singularities
S. Brzostowski, T. Krasiński, G. Oleksik
Let be an isolated singularity at the origin of . One of many invariants that can be associated with is its Łojasiewicz exponent , which me…
A short proof that equisingular plane curve singularities are topologically equivalent
Szymon Brzostowski, Tadeusz Krasiński, Justyna Walewska
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 irr…
Arnold's problem on monotonicity of the Newton number for surface singularities
Szymon Brzostowski, Tadeusz Krasiński, Justyna Walewska
According to the Kouchnirenko theorem, for a generic (precisely non-degenerate in the Kouchnirenko sense) isolated singularity its Milnor number is equal to the Newton n…
The jump of the Milnor number in the X_9 singularity class
Szymon Brzostowski, Tadeusz Krasinski
The jump of the Milnor number of an isolated singularity is the minimal non-zero difference between the Milnor numbers of and one of its deformations We prove…