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 ℂ = (ℂ*)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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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 219–230.
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Ustinovsky, Y.M. Geometry of compact complex manifolds with maximal torus action. Proc. Steklov Inst. Math. 286, 198–208 (2014). https://doi.org/10.1134/S0081543814060108
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DOI: https://doi.org/10.1134/S0081543814060108