On Alexander Polynomials of Certain (2,5) Torus Curves

Details On Alexander Polynomials of Certain (2,5) Torus Curves On Alexander Polynomials of Certain (2,5) Torus Curves

2008-10-08

arxiv.org/abs/0810.1382v1

Mathematics

Algebraic Geometry

Scientific paper

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 f2 = 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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