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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 studyhomology classes represented by algebraic cycles.

A characterization of real holomorphic chains and applications in representing homology classes by algebraic cycles