Momentum polytopes of projective spherical varieties and related Kähler geometry

• Stéphanie Cupit-Foutou ^[1] ; Guido Pezzini ^[3] ; Bart Van Steirteghem ^[2]
  1. [1] Ruhr University Bochum

     Ruhr University Bochum

     Kreisfreie Stadt Bochum, Alemania

     
  2. [2] City University of New York

     City University of New York

     Estados Unidos

     
  3. [3] “Sapienza” Università di Roma, Italia

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-0549-9
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• Resumen

  • We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary and sufficient condition involving momentum polytopes for such manifolds to be Kähler and classify the invariant compatible complex structures of a given Kähler multiplicity free compact and connected Hamiltonian manifold.