Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of real holomorphic chains and applications in
  representing homology classes by algebraic cycles   We show that a $2k$-current $T$ on a complex manifold is a real holomorphic
$k$-chain if and only if $T$ is locally real rectifiable, $d$-closed and has
$\mathcal{H}^{2k}$-locally finite support. This result is applied to study
homology classes represented by algebraic cycles.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga