2025/11/28 by Marwan Bit, Javier González‐Anaya, Bit, Marwan +5
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2511.23456
Gallardo and Routis constructed compactifications of the moduli space of n labeled points in ℙd by assigning weights to points, generalizing Hassett's weighted compactifications of M0,n to higher-dimensional projective spaces. Among their compactifications, there is a toric compactification that generalizes the standard Losev-Manin compactification to this higher-dimensional setting. Our main result identifies the fan of this toric compactification as a symmetric product of a nested fan, generalizing the classical connection between Losev-Manin spaces and the permutohedron to arbitrary dimension. More generally, we prove that the fans of all Gallardo-Routis compactifications that admit reduction maps from this Losev-Manin space are symmetric products of building sets. This shows that the combinatorics of these compactifications are controlled by coarsenings of the permutohedral fan that give rise to Hassett spaces.