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 yn+a(x)y+b(x) = 0, or, equivalently, yn+xαy+xβA(x) = 0 where A(x) is a unit in Ct{x}, α and β are integers, α _ n − 1 and β _ n. The classification was not complete in the most difficult case α n−1 = β n. In the present paper, the classification is extended also in this case, the proofs are improved and some gaps are removed.
Source:
Publications de l'Institut Mathematique, 2007, 81, 95, 69-78
Publisher:
Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd
TY - JOUR
AU - Stepanović, Vanja
AU - Lipkovski, A.
PY - 2007
UR - http://aspace.agrif.bg.ac.rs/handle/123456789/1614
AB - 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 yn+a(x)y+b(x) = 0, or, equivalently, yn+xαy+xβA(x) = 0 where A(x) is a unit in Ct{x}, α and β are integers, α _ n − 1 and β _ n. The classification was not complete in the most difficult case α n−1 = β n. In the present paper, the classification is extended also in this case, the proofs are improved and some gaps are removed.
PB - Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd
T2 - Publications de l'Institut Mathematique
T1 - Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0
EP - 78
IS - 95
SP - 69
VL - 81
UR - https://hdl.handle.net/21.15107/rcub_agrospace_1614
ER -
@article{
author = "Stepanović, Vanja and Lipkovski, A.",
year = "2007",
abstract = "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 yn+a(x)y+b(x) = 0, or, equivalently, yn+xαy+xβA(x) = 0 where A(x) is a unit in Ct{x}, α and β are integers, α _ n − 1 and β _ n. The classification was not complete in the most difficult case α n−1 = β n. In the present paper, the classification is extended also in this case, the proofs are improved and some gaps are removed.",
publisher = "Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd",
journal = "Publications de l'Institut Mathematique",
title = "Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0",
pages = "78-69",
number = "95",
volume = "81",
url = "https://hdl.handle.net/21.15107/rcub_agrospace_1614"
}
Stepanović, V.,& Lipkovski, A.. (2007). Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0. in Publications de l'Institut Mathematique
Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd., 81(95), 69-78.
https://hdl.handle.net/21.15107/rcub_agrospace_1614
Stepanović V, Lipkovski A. Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0. in Publications de l'Institut Mathematique. 2007;81(95):69-78.
https://hdl.handle.net/21.15107/rcub_agrospace_1614 .
Stepanović, Vanja, Lipkovski, A., "Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0" in Publications de l'Institut Mathematique, 81, no. 95 (2007):69-78,
https://hdl.handle.net/21.15107/rcub_agrospace_1614 .
