Wondertopes

Abstract

Positive geometries were introduced by Arkani-Hamed–Bai–Lam in their study of 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 n-pointed stable rational curves ${\bar{M}}_{0,n}$. Thus our work generalizes the known positive geometry ${\bar{M}}_{0,n}$.