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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topological classification of irreducible plane curve singularities in terms of Weierstrass polynomials


Author: Chunghyuk Kang
Journal: Proc. Amer. Math. Soc. 123 (1995), 1363-1371
MSC: Primary 14H20; Secondary 14B05
MathSciNet review: 1291777
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Abstract: Let $ f(z,y)$ be analytically irreducible at 0 and $ f(0) = 0$. Then the plane curve singularity defined by f has the same topological type as the curve defined by $ {f_{k + 1}}$ for some $ k \geq 0$ where $ {f_1} = {z^a} + {y^b},{f_2} = {f_1}^{{n_{21}}} + {y^{{m_{11}}}}{z^{{m_{12}}}},{f_3} = {f_2}^{{n_{31}}} + {f_1}^{{n_{22}}}{y^{{m_{21}}}}{z^{{m_{22}}}}, \ldots $ are defined by induction on k with distinct numerical conditions topologically invariant. Moreover, we give an easy alternate proof of Zariski's topological classification theorem of irreducible plane curve singularities.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1291777-2
PII: S 0002-9939(1995)1291777-2
Article copyright: © Copyright 1995 American Mathematical Society



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