Momentum polytopes of projective spherical varieties and related Kähler geometry
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.08171
 Bibcode:
 2018arXiv180908171C
 Keywords:

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