Moduli Theory of the r-Braid Arrangement

2025/06/22 by Blankers, Vance, Clader, Emily, Halacheva, Iva +2
#14H10 (primary) #14N20 (secondary) #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.18205

Abstract

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 M_0,n, and, in this work, we generalize this result, constructing a moduli space M^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 L^r_n [arXiv:2104.06526], related via a change of weights on the markings.

Citations

• Multimatroids and rational curves with cyclic action
• Wonderful compactifications and rational curves with cyclic action
• De Concini-Procesi wonderful arrangement models - A discrete geometer's point of view
• Moduli spaces of weighted pointed stable curves
• New moduli spaces of pointed curves and pencils of flat connections
• Wonderful models of subspace arrangements

Related

• Building planar polygon spaces from the projective braid arrangement
• Compact moduli of hyperplane arrangements
• The Enumerative Geometry of Hyperplane Arrangements
• Braids, trees, and operads
• A combinatorial model for the moduli of bordered Riemann surfaces and a compactification