(2,3) torus sextics and the Albanese images of 6-fold cyclic multiple planes
The author develops an approach of \textit{Vik. S. Kulikov} [Izv. Ross. Akad. Nauk, Ser. Mat. 59, No. 6, 75-94 (1995; Zbl 0939.14013)] to study the topology of cyclic multiple planes. Such planes are cyclic coverings of \({\mathbb P}^2\) ramified along a curve \(B\) and possibly along the line at infinity. In particular, for an irreducible plane sextic \(B\) with at most simple singularities the author obtains sufficient conditions under which \(B\) is a \((2,3)\) torus curve in the sense of Kulikov. As a consequence irreducible rational plane sextics with simple singularities having cyclic multiples planes of Albanese dimension 2 are described [cf. \textit{H. Tokunaga}, Proc. Am. Math. Soc. 127, No. 7, 1935-1940 (1999; Zbl 0917.14015)].
scientific article; zbMATH DE number 1367786
scientific article