Stacks of uniform cyclic covers of curves and their Picard groups

We study the stack Bh,g,nof 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 Mg. We use this description to compute the integral Picard group of Bh,g,n, showing that it is generated by tautological classes of Bh,g,n