Stacks of ramified Galois covers

Stacks of ramified Galois covers

Abstract: We introduce the notion of Galois cover for a finite group G and discuss the problems of constructing them and of the geometry of the stack G-Cov they form. When G is abelian, we show that these problems are related to the theory of equivariant Hilbert schemes and we describe certain families of G-covers in terms of combinatorial data associated with G. In the general case, we present a correspondence between G-covers and particular monoidal functors and study the problem of Galois covers of normal varieties whose total space is normal.