Geometry of compact complex manifolds with maximal torus action

In this present paper we study geometry of compact complex manifolds equipped with a \emph{maximal} torus $T=(S^1)^k$ action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan $Σ$ and a compelx subgroup $H\subset T_\mathbb C=(\mathbb C^*)^k$. On every manifold $M$ we define the canonical holomorphic foliation $\mathcal F$ and under additional restrictions construct transverse-Kähler form $ω_\mathcal F$. As an application of these constructions, we prove some results on geometry of manifolds~$M$ regarding its analytic subsets.

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