Courants algébriques et courants de Liouville
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 245-271
MSC: 32C25, 32C30, 12D10, 14A20.
DOI: 10.4064/ap86-3-4
Abstract
We define in $\mathbb C^n$ the concepts of algebraic currents and Liouville currents, thus extending the concepts of algebraic complex subsets and Liouville subsets. After having shown that every algebraic current is Liouville, we characterize those positive closed currents on $\mathbb C^n$ which are algebraic. Let $T$ be a closed positive current on $\mathbb C^n$. We give sufficient conditions, relating to the growth of the projective mass of $T$, so that $T$ is Liouville. These results generalize those previously obtained by N. Sibony and P. M. Wong, and K. Takegoshi in the geometrical case, i.e. when $T=[X]$ is the current of integration on an analytical complex subset of $\mathbb C^n$.
