ar X iv : d g - ga / 9 50 60 09 v 1 2 2 Ju n 19 95 Multiplicity - free Hamiltonian actions need not be Kähler
نویسنده
چکیده
In this note we show that Tolman’s example (of a six dimensional Hamiltonian T -space with isolated fixed points and no compatible Kähler structure) can be constructed from the flag variety U(3)/U(1) by U(2)-equivariant symplectic surgery. This implies that Tolman’s space has a “transversal multiplicity-free” action of U(2) and that Delzant’s theorem “every compact multiplicity-free torus action is Kähler” [4] does not generalize to non-abelian actions. Comments and criticisms of this preliminary version are welcome.
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