Toric generalized Kähler structures. I
arXiv: Differential Geometry（2018）
摘要
This is a sequel of , which provides a general formalism for this paper. We mainly investigate thoroughly a subclass of toric generalized Kähler manifolds of symplectic type introduced by Boulanger in . We find torus actions on such manifolds are all strong Hamiltonian in the sense of . For each such a manifold, we prove that besides the ordinary two complex structures J_± associated to the biHermitian description, there is a third canonical complex structure J_0 underlying the geometry, which makes the manifold toric Kähler. We find the other generalized complex structure besides the symplectic one is always a B-transform of a generalized complex structure induced from a J_0-holomorphic Poisson structure β characterized by an anti-symmetric constant matrix. Stimulated by the above results, we introduce a generalized Delzant construction which starts from a Delzant polytope with d faces of codimension 1, the standard Kähler structure of ℂ^d and an anti-symmetric d× d matrix. This construction is used to produce non-abelian examples of strong Hamiltonian actions.
更多查看译文
关键词
kähler structures
AI 理解论文
溯源树
样例
生成溯源树，研究论文发展脉络
Chat Paper
正在生成论文摘要