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The Łojasiewicz exponent via the valuative Hamburger-Noether process
Brzostowski, Szymon 
; (Łódź University Press, 2017)
; (Łódź University Press, 2017)
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 ...
A short proof that equisingular plane curve singularities are topologically equivalent
Brzostowski, Szymon ; Krasinski, Tadeusz ; Walewska, Justyna (Łódź University Press, 2017)
; Krasinski, Tadeusz ; Walewska, Justyna (Łódź University Press, 2017)
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.