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arXiv · 2403.04610

Wondertopes

Sarah Brauner·Christopher Eur·Elizabeth Pratt·Raluca Vlad
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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.

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Sarah Brauner, Christopher Eur, Elizabeth Pratt, Raluca Vlad. 2024-03-07. Wondertopes. https://arxiv.org/abs/2403.04610

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