Journal of the Mathematical Society of Japan

On Alexander polynomials of certain $(2,5)$ torus curves

Masayuki KAWASHIMA and Mutsuo OKA

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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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J. Math. Soc. Japan Volume 62, Number 1 (2010), 213-238.

First available in Project Euclid: 5 February 2010

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Mathematical Reviews number (MathSciNet)

Primary: 14H20: Singularities, local rings [See also 13Hxx, 14B05]
Secondary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14H45: Special curves and curves of low genus

torus curve Alexander polynomial


KAWASHIMA, Masayuki; OKA, Mutsuo. On Alexander polynomials of certain ( 2 , 5 ) torus curves. J. Math. Soc. Japan 62 (2010), no. 1, 213--238. doi:10.2969/jmsj/06210213.

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