On Branched Galois Coverings $(B_1{)}^n\to {\mathbb{P}}^n$

For any $n>1$, we construct examples branched Galois coverings from $M$ to the nth projective space ${\mathbb{P}}^n$ where $M$ is one of $({\mathbb P}^1)^n$,${\mathbb C}^n$or$(B_1)^n$,and$B_1$ is the 1-ball. In terms of orbifolds, this amounts to giving examples of orbifolds over ${\mathbb{P}}^n$ uniformized by $M$.We also discuss the related “orbifold braid groups”.