Multiplicity-free Hamiltonian actions need not be Kähler |
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Authors: | Chris Woodward |
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Affiliation: | (1) Harvard University, Dept. of Mathematics, 1 Oxford Street, Cambridge, M 02138, USA e-mail: woodward@math.harvard.edu, US |
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Abstract: | Multiplicity-free actions are symplectic manifolds with a very high degree of symmetry. Delzant [2] showed that all compact multiplicity-free torus actions admit compatible K?hler structures, and are therefore toric varieties. In this note we show that Delzant's result does not generalize to the non-abelian case. Our examples are constructed by applying U(2)-equivariant symplectic surgery to the flag variety U(3)/T 3. We then show that these actions fail a criterion which Tolman [9] shows is necessary for the existence of a compatible K?hler structure. Oblatum IX-1995 & 21-IV-1997 |
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