Deformations of singularities of plane curves. Topological approach

2009/07/23 by Maciej Borodzik, Borodzik, Maciej · 1 citation
Computer Science · Mathematics · #14H10 #14H20 #57M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.AG #math.GT #msc:14H10 #msc:14H20 #msc:57M25

paper · pdf · doi:10.48550/arxiv.0907.4129

7 pages. Last part rewritten for better readability (hopefully)

openalex publication_date 2009/07/23 · arxiv created 2009/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use a knot invariant, namely the Tristram--Levine signature to study deformations of singular points of plane curves. We find a bound on the sum of M numbers over all singularities of a generic fiber in terms of the M number of the singularity at the central fiber and some topological data.

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