Geometry of irreducible plane quartics and their quadratic residue conics

2009/11/30 by Hiro‐o Tokunaga, Hiroo Tokunaga, Tokunaga, Hiroo
Computer Science · Mathematics · #14E20 #14J27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Polynomial and algebraic computation #math.AG #msc:14E20 #msc:14J27

paper · pdf · doi:10.48550/arxiv.0911.5540

arxiv created 2009/11/30 · openalex publication_date 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be an irreducible plane curve. In this article, we first introduce a notion of a quadratic residue curve mod D, and study quadratic residue concis C mod an irreducible quartic curve Q. As an application, we study a dihedral cover of P² with branch locus C+Q and give two examples of Zariski pairs as by-products.

Citations

• Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics

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• On the topology of the complements of reducible plane curves via Galois covers
• Limits of pluri-tangent planes to quartic surfaces
• Geometry of bisections of elliptic surfaces and Zariski N-plets II
• A note on the topology of arrangements for a smooth plane quartic and its bitangent lines