On Alexander polynomials of certain $(2,5)$ torus curves
Masayuki KAWASHIMA and Mutsuo OKA
Source: J. Math. Soc. Japan Volume 62, Number 1
(2010), 213-238.
Abstract
In this paper, we compute Alexander polynomials of a torus curve $C$ of type $(2,5)$, $C:\,f(x,y)=f_{2}(x,y)^{5}+f_{5}(x,y)^{2}=0$, under the assumption that the origin $O$ is the unique inner singularity and $f_{2}=0$ is an irreducible conic. We show that the Alexander polynomial remains the same with that of a generic torus curve as long as $C$ is irreducible.
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1265380429
Digital Object Identifier: doi:10.2969/jmsj/06210213
Zentralblatt MATH identifier: 05682672
Mathematical Reviews number (MathSciNet): MR2648221
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