On Alexander polynomials of torus curves

Abstract

Let p and q be integers such that p > q ≥q 2 and q divides p. Let \varphi (q) be the Euler number of q. We exhibit a Zariski \varphi(q)-ple, distinguished by the Alexander polynomial, whose curves are tame torus curves of type (p, q), with q smooth irreducible components of degree p, and one single singular point topologically equivalent to the Brieskorn-Pham singularity\ \ v^q+u^{qp^2}=0.