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.
- Pub Date:
- September 2018
- Mathematics - Algebraic Geometry;
- Mathematics - Representation Theory;
- Mathematics - Symplectic Geometry
- v1: 32 pages. v2: 47 pages, fixed errors, improved exposition, expanded Section 7. v3: 47 pages, implemented changes and corrections requested by referee