Complex Manifolds (Sep 2021)

Real rectifiable currents, holomorphic chains and algebraic cycles

  • Teh Jyh-Haur,
  • Yang Chin-Jui

DOI
https://doi.org/10.1515/coma-2020-0119
Journal volume & issue
Vol. 8, no. 1
pp. 274 – 285

Abstract

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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