Wedge product of positive currents and balanced manifolds

Abstract

We define on a manifold $X$ a wedge product $S \wedge T$ of a closed positive (1,1)-current $S$, smooth outside a proper analytic subset $Y$ of $X$, and a positive pluriharmonic $(k,k)$-current $T$, when $k$ is less than the codimension of $Y$. Using this tool, we prove that if $M$ is a compact complex manifold of dimension $n \geq 3$, which is Kähler outside an irreducible curve, then $M$ carries a balanced metric.