Wondertopes
Algebraic Geometry
2025-10-13 v2 Combinatorics
Abstract
Positive geometries were introduced by Arkani-Hamed--Bai--Lam as a method of computing scattering amplitudes in theoretical physics. We show that a positive geometry from a polytope admits a log resolution of singularities to another positive geometry. Our result states that the regions in a wonderful compactification of a hyperplane arrangement complement, which we call wondertopes, are positive geometries. A familiar wondertope is the curvy associahedron, which tiles the moduli space of pointed stable rational curves. Thus our work generalizes the known positive geometry structure on this moduli space.
Keywords
Cite
@article{arxiv.2403.04610,
title = {Wondertopes},
author = {Sarah Brauner and Christopher Eur and Elizabeth Pratt and Raluca Vlad},
journal= {arXiv preprint arXiv:2403.04610},
year = {2025}
}
Comments
33 pages, 10 figures; comments welcome! v2: to appear in AiM