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

2008/10/08 by M. Kawashima, Masayuki Kawashima, M. Oka +3
Mathematics · #14H20 #14H30 #14H45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14H20 #msc:14H30 #msc:14H45

paper · pdf · doi:10.48550/arxiv.0810.1382

arxiv created 2008/10/08 · openalex publication_date 2008/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we compute Alexander polynomials of a torus curve C of type (2, 5), C : f(x, y) = f₂(x, y)⁵ + f₅(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.

Citations

• Classification of Local Singularities on Torus Curves of Type (2,5)

Related

• On the Alexander polynomials of Hurwitz curves
• Twisted Alexander Polynomials of Hypersurface Complements
• Mordell-Weil groups of elliptic threefolds and the Alexander module of plane curves
• The Alexander polynomial of a plane curve singularity via the ring of functions on it
• Alexander polynomial of sextics