On the topology of the complements of reducible plane curves via Galois covers

2013/04/02 by Shinzo Bannai, Bannai, Shinzo, Masayuki Kawashimaand +3
Mathematics · #14E20 #17J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT #msc:14E20 #msc:17J27

paper · pdf · doi:10.48550/arxiv.1304.0536

17 pages

arxiv created 2013/04/02 · arxiv updated 2013/04/03

Abstract

Let \mathcal B be a reducible reduced plane curve. We introduce a new point of view to study the topology of (\PP², \mathcal B) via Galois covers and Alexander polynomials. We show its effectiveness through examples of Zariski N-plets for conic and conic-quartic configurations.

Related

• A note on splitting numbers for Galois covers and π₁-equivalent Zariski k-plets
• Lectures on topology of complements and fundamental groups
• Simultaneous Galois points for a reducible plane curve consisting of nonsingular components
• Galois covers of graphs and embedded topology of plane curves
• Geometry of irreducible plane quartics and their quadratic residue conics