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VOL. 63 | 2012 A note on quadratic residue curves on rational ruled surfaces
Hiro-o Tokunaga

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

## Abstract

Let $\Sigma$ be a smooth projective surface, let $f':S'\to\Sigma$ be a double cover of $\Sigma$ and let $\mu :S\to S'$ be the canonical resolution of $S'$. Put $f = f'\circ\mu$. An irreducible curve $D$ on $\Sigma$ is said to be a splitting curve with respect to $f$ if $f^*D$ is of the form $D^+ + D^- + E$, where $D^+ \neq D^-$, $D^- = \sigma_f^* D^+$, $\sigma_f$ being the covering transformation of $f$ and all irreducible components of $E$ are contained in the exceptional set of $\mu$. In this article, we consider "reciprocity" concerning splitting curves when $\Sigma$ is a rational ruled surface.

## Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1325.14028
MathSciNet: MR3051255

Digital Object Identifier: 10.2969/aspm/06310565

Subjects:
Primary: 14E20, 14G99