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arXiv · 1809.08171

Momentum polytopes of projective spherical varieties and related K\"ahler geometry

Stéphanie Cupit-Foutou·Guido Pezzini·Bart Van Steirteghem
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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 K\"ahler and classify the invariant compatible complex structures of a given K\"ahler multiplicity free compact and connected Hamiltonian manifold.

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Stéphanie Cupit-Foutou, Guido Pezzini, Bart Van Steirteghem. 2018-09-21. Momentum polytopes of projective spherical varieties and related K\"ahler geometry. https://doi.org/10.1007/s00029-020-0549-9

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