Examples of non-Kahler Hamiltonian torus actions

• 成果类型: Article
• 署名作者: Tolman, S
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050205
• 发表日期: 1998
• 页码: 299-310
• 关键词: convexity; MANIFOLDS

摘要

An important question with a rich history is the extent to which the symplectic category is larger than the Kahler category. Many interesting examples of non-Kahler symplectic manifolds have been constructed [T] [M] [G]. However, sufficiently large symmetries can force a symplectic manifolds to be Kahler [D] [Kn]. In this paper, we solve several outstanding problems by constructing the first symplectic manifold with large non-trivial symmetries which does not admit an invariant Kahler structure. The proof that it is not Kahler is based on the Atiyah-Guillemin-Sternberg convexity theorem [At] [GS]. Using the ideas of this paper, C. Woodward shows that even the symplectic analogue of spherical varieties need not be Kahler [W].