Analytic types of plane curve singularities defined by weighted homogeneous polynomials
Author:
Chunghyuk Kang
Journal:
Trans. Amer. Math. Soc. 352 (2000), 39954006
MSC (2000):
Primary 32S15, 14E15
Published electronically:
February 25, 2000
MathSciNet review:
1661266
Fulltext PDF Free Access
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Abstract: We classify analytically isolated plane curve singularities defined by weighted homogeneous polynomials , which are not topologically equivalent to homogeneous polynomials, in an elementary way. Moreover, in preparation for the proof of the above analytic classification theorem, assuming that either satisfies the same property as the above does or is homogeneous, then we prove easily that the weights of the above determine the topological type of and conversely. So, this gives another easy proof for the topological classification theorem of quasihomogenous singularities in , which was already known. Also, as an application, it can be shown that for a given , where is a quasihomogeneous holomorphic function with an isolated singularity at the origin or with a positive integer , analytic types of isolated hypersurface singularities defined by are easily classified where is defined just as above.
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Additional Information
Chunghyuk Kang
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151–742, Korea
Email:
chkang@math.snu.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002994700024788
PII:
S 00029947(00)024788
Received by editor(s):
May 5, 1998
Published electronically:
February 25, 2000
Additional Notes:
Supported by MOE, Project No. BSRI971413 and GARCKOSEF, 1998. Also supported in part by the SNU97031061
Article copyright:
© Copyright 2000
American Mathematical Society
