Real rectifiable currents, holomorphic chains and algebraic cycles

Abstract

We study some fundamental properties of real rectifiable currents and give a generalization of King’s theorem to characterize currents defined by positive real holomorphic chains. Our main tool is Siu’s semi-continuity theorem and our proof largely simplifies King’s proof. A consequence of this result is a sufficient condition for the Hodge conjecture.

Keywords

• real rectifiable current
• real holomorphic chain
• holomorphic subvariety
• hodge conjecture
• 32u40
• 14c25