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

Abstract

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 ℋ2k-locally finite support. This result is applied to study homology classes represented by algebraic cycles.

Keywords

• rectifiable current
• holomorphic chain
• algebraic cycle
• 32c30
• 32c35
• 14c25