Geometry of compact complex manifolds with maximal torus action |
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Authors: | Yu M Ustinovsky |
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Institution: | 1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
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Abstract: | We study the geometry of compact complex manifolds M equipped with a maximal action of a torus T = (S 1) k . We present two equivalent constructions that allow one to build any such manifold on the basis of special combinatorial data given by a simplicial fan Σ and a complex subgroup H ? T ? = (?*) k . On every manifold M we define a canonical holomorphic foliation F and, under additional restrictions on the combinatorial data, construct a transverse Kähler form ω F . As an application of these constructions, we extend some results on the geometry of moment-angle manifolds to the case of manifolds M. |
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