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

 

The Łojasiewicz exponent of an isolated weighted homogeneous surface singularity


Authors: Tadeusz Krasinski, Grzegorz Oleksik and Arkadiusz Płoski
Journal: Proc. Amer. Math. Soc. 137 (2009), 3387-3397
MSC (2000): Primary 32S05
Published electronically: May 6, 2009
MathSciNet review: 2515408
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Abstract: We give an explicit formula for the Łojasiewicz exponent of an isolated weighted homogeneous surface singularity in terms of its weights. From the formula we get that the Łojasiewicz exponent is a topological invariant of these singularities.


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Additional Information

Tadeusz Krasinski
Affiliation: Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Email: krasinsk@uni.lodz.pl

Grzegorz Oleksik
Affiliation: Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Email: oleksig@math.uni.lodz.pl

Arkadiusz Płoski
Affiliation: Department of Mathematics, Technical University, Al. 1000 LPP 7, 25-314 Kielce, Poland
Email: matap@tu.kielce.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09935-3
PII: S 0002-9939(09)09935-3
Keywords: Łojasiewicz exponent, weighted homogeneous polynomial, isolated surface singularity, polar curve.
Received by editor(s): July 10, 2008
Received by editor(s) in revised form: February 10, 2009
Published electronically: May 6, 2009
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2009 American Mathematical Society