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Multiplicity-free Hamiltonian actions need not be Kähler

Chris Woodward
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Abstract

We show that Tolman's example (of a six dimensional Hamiltonian $T^2$-space with isolated fixed points and no compatible Kähler structure) can be constructed from the flag variety $U(3)/U(1)^3$ 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'' \cite{D1} does not generalize to non-abelian actions.

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BibTeXRIS

Chris Woodward. 1995-06-22. Multiplicity-free Hamiltonian actions need not be Kähler. https://arxiv.org/abs/dg-ga/9506009

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