2015/01/24 by Kaiho Tommy Wong, Wong, Kaiho Tommy
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1501.06065
openalex publication_date 2015/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define twisted Alexander polynomials of a complex hypersurface with arbitrary singularities. These generalize the classical Alexander polynomials of high dimensional hypersurfaces and the twisted Alexander polynomial of plane curves. We recover the classical torsionness and divisibility results, which say that, under certain assumptions, the twisted Alexander modules of a complex hypersurface are torsion modules, and that their orders, the twisted Alexander polynomials, divide the product of certain `local polynomials' defined in terms of the topology near singularities.