Geodesic
Geometry of compact complex manifolds with maximal torus action
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 219-230.

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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 $\Sigma$ and a complex subgroup $H\subset T_\mathbb C=(\mathbb C^*)^k$. On every manifold $M$ we define a canonical holomorphic foliation $\mathcal F$ and, under additional restrictions on the combinatorial data, construct a transverse Kähler form $\omega _\mathcal F$. As an application of these constructions, we extend some results on the geometry of moment–angle manifolds to the case of manifolds $M$. 
@article{TM_2014_286_a9,
     author = {Yu. M. Ustinovsky},
     title = {Geometry of compact complex manifolds with maximal torus action},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/TM_2014_286_a9/}
}
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Yu. M. Ustinovsky. Geometry of compact complex manifolds with maximal torus action. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 219-230. http://geodesic.mathdoc.fr/item/TM_2014_286_a9/

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