Geometry of irreducible plane quartics and their quadratic residue conics

Details Geometry of irreducible plane quartics and their quadratic residue conics Geometry of irreducible plane quartics and their quadratic residue conics

2009-11-30

arxiv.org/abs/0911.5540v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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