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

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.