Geometry of irreducible plane quartics and their quadratic residue conics

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 $P^2$ with branch locus $C+Q$ and give two examples of Zariski pairs as by-products.

References in corpus (1)

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