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Peer-reviewedCC BY 4.0Algebraic Combinatorics

Geometry of Adjoint Hypersurfaces for Polytopes

  • Clemens Brüser1
  • Julian Weigert2
  1. 1Technische Universität Dresden, Germany
  2. 2Max Planck Institute for Mathematics in the Sciences, Leipzig, and Georg-August-Universität Göttingen, Germany
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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 [9, Problem 2] and generalizes their main Theorem [9, Theorem 1] 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.

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Cite

BibTeXRIS
BibTeX
@article{bruser2026geometry,
  title = {{Geometry of Adjoint Hypersurfaces for Polytopes}},
  author = {Clemens Brüser and Julian Weigert},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.516},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.516/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Geometry of Adjoint Hypersurfaces for Polytopes
AU  - Clemens Brüser
AU  - Julian Weigert
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.516
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.516/
AB  - 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 [9, Problem 2] and generalizes their main Theorem [9, Theorem 1] 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.
SN  - 2589-5486
ER  -