Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex manifolds with maximal torus actions   In this paper, we introduce the notion of maximal actions of compact tori on
smooth manifolds and study compact connected complex manifolds equipped with
maximal actions of compact tori. We give a complete classification of such
manifolds, in terms of combinatorial objects, which are triples $(\Delta,
\mathfrak{h}, G)$ of nonsingular complete fan $\Delta$ in $\mathfrak{g}$,
complex vector subspace $\mathfrak{h}$ of $\mathfrak{g}^{\mathbb{C}}$ and
compact torus $G$ satisfying certain conditions. We also give an equivalence of
categories with suitable definitions of morphisms in these families, like toric
geometry.
  We obtain several results as applications of our equivalence of categories;
complex structures on moment-angle manifolds, classification of holomorphic
nondegenerate $\mathbb{C}^n$-actions on compact connected complex manifolds of
complex dimension $n$, and construction of concrete examples of non-K\"{a}hler
manifolds.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int