Multiplicity-free Hamiltonian actions need not be Kahler
成果类型：
Article
署名作者：
Woodward, C
署名单位：
Harvard University
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s002220050206
发表日期：
1998
页码：
311-319
关键词：
摘要：
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 Kahler 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 Kahler structure.
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