Definition of being nef and big On a compact Kähler manifold $M$, given a real $(1,1)$ form $\alpha$ we say that it is nef if it is in the closure of the Kähler cone. Moreover, if $\int_{M} \alpha^n > 0$ we say that it is big. However, what is the orientation chosen here for $M$?

The volume form is given by $\omega^n/n!$, where $\omega$ is the Kähler form.