2018/10/18 by Yicao Wang, Wang, Yicao · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.DG #msc:53D05 #msc:53D18 #msc:53D20
paper · pdf · doi:10.48550/arxiv.1810.08265
41 pages, no figures
arxiv created 2018/10/18 · arxiv updated 2018/10/22
This is a sequel of \citeWang, which provides a general formalism for this paper. We mainly investigate thoroughly a subclass of toric generalized Kahler manifolds of symplectic type introduced by Boulanger in \citeBou. We find torus actions on such manifolds are all strong Hamiltonian in the sense of \citeWang. 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 J0 underlying the geometry, which makes the manifold toric Kahler. We find the other generalized complex structure besides the symplectic one is always a B-transform of a generalized complex structure induced from a J0-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 Kahler structure of ℂd and an anti-symmetric d× d matrix. This construction is used to produce non-abelian examples of strong Hamiltonian actions.