Geometry of Adjoint Hypersurfaces for Polytopes

2025/11/17 by Brüser, Clemens, Weigert, Julian · 1 citation
#14J70 #14N20 #52B11 #52B40 14Q30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.13537

Abstract

In this article we prove that the adjoint polynomial of arbitrary convex polytopes is up to scaling uniquely determined by vanishing to the right order on the polytopes residual arrangement. This answers a problem posed by Kohn and Ranestad and generalizes their main theorem to non-simple polytopes. We furthermore prove that the adjoint polynomial is already characterized by vanishing to the right order on a zero-dimensional subset of the residual arrangement.

Citations

• Adjoints of Polytopes: Determinantal Representations and Smoothness
• Canonical forms of polytopes from adjoints
• Toric Amplitudes and Universal Adjoints
• What is Positive Geometry?
• An invitation to positive geometries
• Projective geometry of Wachspress coordinates
• S-hypersimplices, pulling triangulations, and monotone paths

Cited by

• Log Canonical Models and Positive Geometries

Related

• Adjoints of Polytopes: Determinantal Representations and Smoothness
• Canonical forms of polytopes from adjoints
• Projective geometry of Wachspress coordinates
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• Positive Polytopes with Few Facets in the Grassmannian