Stacks of uniform cyclic covers of curves and their Picard groups

We study the stack B h,g,n of uniform cyclic covers of degree n between smooth curves of genus h and g and, for h >> g, present it as an open substack of a vector bundle over the universal Jacobian stack of M g . We use this description to compute the integral Picard group of B h,g,n , showing that it is generated by tautological classes of B h,g,n .