  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
$\Sigma$ 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-K\"{a}hler form
$\omega_\mathcal F$. As an application of these constructions, we prove some
results on geometry of manifolds~$M$ regarding its analytic subsets.

Complex Variables