Tohoku Mathematical Journal
2008
March
SECOND SERIES VOL. 60, NO. 1

Tohoku Math. J.
60 (2008), 123-134

Title WEDGE PRODUCT OF POSITIVE CURRENTS AND BALANCED MANIFOLDS

Author Lucia Alessandrini and Giovanni Bassanelli

(Received October 16, 2006, revised July 20, 2007)
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.

2000 Mathematics Subject Classification. Primary 32J27; Secondary 32U40, 32J17.
Key words and phrases. Wedge product of currents, positive currents, plurisubharmonic currents, Kähler manifolds, balanced manifolds.

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