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.

Momentum polytopes of projective spherical varieties and related Kähler geometry / Cupit-Foutou, S.; Pezzini, G.; VanSteirteghem, B.. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - 26:2(2020).

Momentum polytopes of projective spherical varieties and related Kähler geometry

Pezzini G.;
2020

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/1406293
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