The relative Brauer group of a cyclic cover of affine space

We study the finite-dimensional central division algebras over the rational function field in several variables over an algebraically closed field. We describe the division algebras that are split by the cyclic covering obtained by adjoining the nth root of a polynomial. The relative Brauer group is described in terms of the Picard group of the cyclic covering and its Galois group. Many examples are given and in most cases division algebras are presented that represent generators of the relative Brauer group.