Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$\Sigma$ 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.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio