Definition 5.19.154DFBEC43A4B0

Definition 5.19.15.4DFBEC43A4B0 A class $\alpha \in \mathrm{H}^{1,1}(X,\mathbb {R})$ is modified nef if the following condition holds: after fixing a reference Kähler metric $\omega $ on $X$, for any $\epsilon >0$, we can find a closed $(1,1)$-current $T\in \alpha $ such that

1. EEF77CF757EA

   $T+\epsilon \omega \geq 0$;

2. AEF6FAE47DAC

   $\nu (T+\epsilon \omega ,D)=0$ for any prime divisor $D$ on $X$.

This definition is independent of the choice of $\omega $.