Blankers, Clader, Halacheva, Liu, Ross — Moduli Theory Of The $R$-Braid Arrangement (2025)

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 \(\overline{\mathcal{ M}}_{ 0,n}\), and, in this work, we generalize this result, constructing a moduli space \(\overline{\mathcal{ M}}\textasciicircum r_{ n}\) of certain genus-zero curves with an order-\(r\) involution 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 \(\overline{\mathcal{ L}}\textasciicircum r_n\) [arXiv:2104.06526], related via a change of weights on the markings.