Cristin-resultat-ID: 1956821
Sist endret: 20. november 2021, 17:33
Resultat
Vitenskapelig artikkel
2021

Adjoints and canonical forms of polypols

Bidragsytere:
  • Ragni Piene
  • Kathlén Kohn
  • Kristian Ranestad
  • Felix Rydell
  • Boris Shapiro
  • Rainer Sinn
  • mfl.

Tidsskrift

arXiv.org
ISSN 2331-8422

Om resultatet

Vitenskapelig artikkel
Publiseringsår: 2021
Artikkelnummer: 2108.11747

Beskrivelse Beskrivelse

Tittel

Adjoints and canonical forms of polypols

Sammendrag

Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an algebro-geometric perspective. We relate planar polypols to positive geometries introduced originally in particle physics, and identify the adjoint curve of a planar polypol with the numerator of the canonical differential form associated with the positive geometry. We settle several cases of a conjecture by Wachspress claiming that the adjoint curve of a regular planar polypol does not intersect its interior. In particular, we provide a complete characterization of the real topology of the adjoint curve for arbitrary convex polygons. Finally, we determine all types of planar polypols such that the rational map sending a polypol to its adjoint is finite, and explore connections of our topic with algebraic statistics

Bidragsytere

Aktiv cristin-person

Ragni Piene

  • Tilknyttet:
    Forfatter
    ved Algebra, geometri og topologi ved Universitetet i Oslo

Kathlén Kohn

  • Tilknyttet:
    Forfatter

Kristian Ranestad

  • Tilknyttet:
    Forfatter
    ved Algebra, geometri og topologi ved Universitetet i Oslo

Felix Rydell

  • Tilknyttet:
    Forfatter

Boris Shapiro

  • Tilknyttet:
    Forfatter
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