Geometry of irreducible plane quartics and their quadratic residue conics

Hiro-o TOKUNAGA

Journal of Singularities
volume 2 (2010), 170-190
Proceedings of Singularities in Aarhus, August 2009

Received: 20 November 2009

DOI: 10.5427/jsing.2010.2k

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Abstract:

Let D be an irreducible plane curve in P^2. In this article, we first introduce a notion of a quadratic residue curve mod D, and study quadratic residue conics 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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Author(s) information:

Hiro-o TOKUNAGA
Department of Mathematics and Information Sciences
Graduate School of Science and Engineering
Tokyo Metropolitan University
1-1 Minami-Ohsawa, Hachiohji 192-0397 JAPAN
email: tokunaga@tmu.ac.jp