Triple covers of algebraic surfaces and a generalization of Zariski’s example. (English) Zbl 1198.14016

Ishida, Hirotaka; Tokunaga, Horo-o

Brasselet, Jean-Paul (ed.) et al., Singularities, Niigata–Toyama 2007. Proceedings of the 4th Franco-Japanese symposium, Niigata, Toyama, Japan, August 27–31, 2007. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-55-6/hbk). Advanced Studies in Pure Mathematics 56, 169-185 (2009).

It is a classical result due to Zariski that a complex plane sextic \(C\) with 6 cusps is the branch locus of a non Galois triple cover of the plane if and only if it is defined by an equation of the form \(A^3+B^2=0\) where \(A\) and \(B\) are homogeneous polynomials of degree respectively \(2\) and \(3\). The paper under review contains an extension of this result to the case of a plane sextic with at most simple singularities.
For the entire collection see [Zbl 1181.00034].

Reviewer: Rita Pardini (Pisa)

MSC:

14E20	Coverings in algebraic geometry
14J17	Singularities of surfaces or higher-dimensional varieties

Keywords:

triple cover; cubic surface; plane sextic; torus curve