Analytic Equivalence of Plane Curve Singularities y^{n}+x^{alpha}y+x^{beta}a(x)=0
Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 69
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
There are not many examples of complete analytical classification of specific
families of singularities, even in the case of plane algebraic curves. In
1989, Kang and Kim published a paper on analytical classification of plane
curve singularities $y^{n}+a(x)y+b(x)=0$, or, equivalently,
$y^{n}+x^{\alpha}y+x^{\beta}A(x)=0$ where $A(x)$
is a unit in $\mathbb{C}t\{x\}$, $\alpha$ and $\beta$ are
integers, $\alpha\geq n-1$ and $\beta\geq n$. The classification was not
complete in the most difficult case $\frac{\alpha}{n-1}=\frac{\beta}{n}$. In
the present paper, the classification is extended also in this case, the
proofs are improved and some gaps are removed.
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author = {A. Lipkovski and V. Stepanovi\'c},
title = {Analytic {Equivalence} of {Plane} {Curve} {Singularities} y^{n}+x^{alpha}y+x^{beta}a(x)=0},
journal = {Publications de l'Institut Math\'ematique},
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A. Lipkovski; V. Stepanović. Analytic Equivalence of Plane Curve Singularities y^{n}+x^{alpha}y+x^{beta}a(x)=0. Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 69 . doi: 10.2298/PIM0795069S
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