Tangential Alexander polynomials and non-reduced degeneration

2006/01/11 by Mutsuo Oka, Oka, Mutsuo
Mathematics · #14H30 #14H45 #32S55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14H30 #msc:14H45 #msc:32S55

paper · pdf · doi:10.48550/arxiv.math/0601236

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openalex publication_date 2006/01/11 · arxiv created 2006/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with θ^Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration C_t → D₀+jL. We show that there exists a certain surjectivity of the fundamental groups and divisibility among their Alexander polynomials.

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