Moduli Theory of the r -Braid Arrangement

We describe a family of hyperplane arrangements depending on a positive integer parameter r , which we refer to as the r -braid arrangements, and which can be viewed as a generalization of the classical braid arrangement. The wonderful compactification of the braid arrangement (with respect to its minimal building set) is well-known to yield the moduli space M̄0,n , and, in this work, we generalize this result, constructing a moduli space M̄ʳₙ of certain genus-zero curves with an order- r automorphism that we identify with the corresponding wonderful compactification of the r -braid arrangement. The resulting space is a variant of the previously studied moduli space L̄ʳₙ of [CDH + 22], related via a change of weights on the markings.