Geodesic
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 .

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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.
DOI : 10.2298/PIM0795069S
Classification : 14B05 14H20 32S15 
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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. http://geodesic.mathdoc.fr/articles/10.2298/PIM0795069S/

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