6 papers
Jump of the Milnor Number in Linear Deformations with Fixed Order
Tadeusz Krasiński, Aleksandra Zakrzewska
Let be a plane curve singularity. We study the jump of the Milnor number of a homogeneous singularity of order in the class of linear deformations $f_{s}=f_{0}+…
A note on the paper "The Cremona problem in dimension 2" by Wolfgang Bartenwerfer
Szymon Brzostowski, Tadeusz Krasiński
The paper titled "Cremona problem in dimension 2" by W. Bartenwerfer presented a flawed attempt at proving the Jacobian Conjecture. Our aim is to provide a thorough analysis of the…
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…
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…
Non-degenerate jump of Milnor numbers of surface singularities
Szymon Brzostowski, Tadeusz Krasiński, Justyna Walewska
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 give a…