On metabelian galois coverings of complex algebraic varieties

Abstract

Let $f:X\to Y$ be a finite ramified Galois covering of algebraic varieties defined over the complex numbers. In this paper, we prove some structure theorems for such coverings in the case that the non-abelian Galois group of the cover is metabelian (in particular metacyclic). Our results extend the previous ones, obtained by several authors, in the case of abelian and dihedral Galois coverings. In analogy with the abelian (and generalizing the dihedral) case, we find "building data" of metabelian covers from which the cover can be reconstructed. In addition to analyzing several examples, we compute invariants and eigensheaves of the group actions of the coverings under study with some applications.

20 pages

References in corpus (2)

• Dihedral Galois covers of algebraic varieties and the simple cases
• On the Prym map of Galois covering

Cited by in corpus (1)

• On the Prym map of Galois covering