Description:
<jats:title>Abstract</jats:title><jats:p>We show that a 2<jats:italic>k</jats:italic>-current <jats:italic>T</jats:italic> on a complex manifold is a real holomorphic <jats:italic>k</jats:italic>-chain if and only if <jats:italic>T</jats:italic> is locally real rectifiable, <jats:italic>d</jats:italic>-closed and has ℋ<jats:sup>2</jats:sup><jats:italic><jats:sup>k</jats:sup></jats:italic>-locally finite support. This result is applied to study homology classes represented by algebraic cycles.</jats:p>