Automorphisms of multiplicity free Hamiltonian manifolds

Details Automorphisms of multiplicity free Hamiltonian manifolds Automorphisms of multiplicity free Hamiltonian manifolds

2010-02-23

arxiv.org/abs/1002.4256v3

J. Amer. Math. Soc. 24 (2011), 567-601

Mathematics

Symplectic Geometry

v1: 42 pages; v2: 42 pages, abstract added, minor changes; v3: 43 pages, Corollary 11.4 added, minor changes

Scientific paper

10.1090/S0894-0347-2010-00686-8

We compute the sheaf of automorphisms of a multiplicity free Hamiltonian
manifold over its momentum polytope and show that its higher cohomology groups
vanish. Together with a theorem of Losev, arXiv:math/0612561, this implies a
conjecture of Delzant: a compact multiplicity free Hamiltonian manifold is
uniquely determined by its momentum polytope and its principal isotropy group.

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