Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0
Апстракт
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.
Извор:
Publications de l'Institut Mathematique, 2007, 81, 95, 69-78Издавач:
- Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd
Институција/група
Poljoprivredni fakultetTY - 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 .