Remark 20.2.11F5CDFD8547BC

Remark 20.2.11.F5CDFD8547BC As in 5.19.5, the trace operator could also be applied to closed positive $(1,1)$-currents on $X$. If $T\in \mathcal{Z}_+(X,\alpha )$ for some pseudo-effective class $\alpha $ on $X$ (see definition 5.19.3) and $\beta \in \mathrm{H}^{1,1}(\widetilde{Y},\mathbb {R})$, then we write

for any (if exists) closed positive $(1,1)$-current in $\beta $ representing $\operatorname{Tr}_ Y(T)$ when $\nu (T,Y)=0$.