Dihedral sign patterns in M_0,n

2025/08/20 by Cortes, Veronica Calvo, Hannah Tillmann-Morris, Tillmann-Morris, Hannah
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2508.14714

openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

The connected components of M_0,n(ℝ) are in bijection with the (n-1)!/2 dihedral orderings of [n]. They are all isomorphic. We construct monomial maps between them, and use these maps to prove a conjecture of Arkani-Hamed, He, and Lam in the case of M_0,n. Namely, we provide a bijection between connected components and sign patterns that are consistent with the extended u-relations for the dihedral embedding.

Citations

• What is Positive Geometry?
• Tropicalizing binary geometries
• Binary geometries from pellytopes
• Moduli spaces in positive geometry
• Positive del Pezzo Geometry
• Scattering amplitudes of stable curves
• Stringy Canonical Forms
• Algebraic Geometry of Bayesian Networks

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