Real rectifiable currents, holomorphic chains and algebraic cycles

2018/09/30 by Teh, Jyh-Haur, Yang, Chin-Jui
#14C30 #53C65 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.00355

Abstract

We study some fundamental properties of real rectifiable currents and give a generalization of King's theorem in characterizing currents defined by positive real holomorphic chains. Our proof uses Siu's semicontinuity theorem and largely simplifies King's proof. A consequence of this result is a sufficient condition for the Hodge conjecture.

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