Momentum polytopes of projective spherical varieties and related Kähler geometry
arXiv:1809.08171 · doi:10.1007/s00029-020-0549-9
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.
v1: 32 pages. v2: 47 pages, fixed errors, improved exposition, expanded Section 7. v3: 47 pages, implemented changes and corrections requested by referee
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