Definition 13.11.1005C17B17762F

Definition 13.11.10.05C17B17762F Let $T_1,\ldots ,T_ p$ be closed positive $(1,1)$-currents on $X$. We say that $T_1\wedge \cdots \wedge T_ p$ is well-defined if there exists an open covering $\mathcal{U}$ of $X$ such that on each $U\in \mathcal{U}$, we can find $\varphi _ j^ U\in \mathrm{PSH}(U)$ ($j=1,\ldots ,p$) such that

and $\mathrm{dd}^{\mathrm{c}}\varphi _1^ U\wedge \cdots \wedge \mathrm{dd}^{\mathrm{c}}\varphi _ p^ U$ is well-defined. In this case, we define the non-pluripolar product $T_1\wedge \cdots \wedge T_ p$ as the closed positive $(p,p)$-current on $X$ defined by