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VOL. 56 | 2009 Triple covers of algebraic surfaces and a generalization of Zariski's example
Hirotaka Ishida, Hiro-o Tokunaga

Editor(s) Jean-Paul Brasselet, Shihoko Ishii, Tatsuo Suwa, Michel Vaquie

Abstract

Let $B$ be a reduced sextic curve in $\mathbb{P}^2$. In the case when singularities of $B$ are only six cusps, Zariski proved that there exists a non-Galois triple cover branched at $B$ if and only if $B$ is given by an equation of the form $G_2^3 + G_3^2$, where $G_i$ denotes a homogeneous polynomial of degree $i$. In this article, we generalize Zariski's statement to any reduced sextic curve with at worst simple singularities. To this purpose, we give formulae for numerical invariants of non-Galois triple covers by using Tan's canonical resolution.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1198.14016
MathSciNet: MR2604082

Digital Object Identifier: 10.2969/aspm/05610169

Subjects:
Primary: 14E20, 14J17

Rights: Copyright © 2009 Mathematical Society of Japan

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