Definition 10.4.1CFDE52E42C6B

Definition 10.4.1.CFDE52E42C6B A class $\alpha \in H^{1,1}(X,\mathbb R)$ is

• pseudo-effective if it contains a closed positive current;

• Kähler if it contains a Kähler form;

• nef if for every $\varepsilon >0$ it contains a smooth form $\theta _\varepsilon $ with $\theta _\varepsilon \geq -\varepsilon \omega $;

• big if it contains a closed current $T$ with $T\geq \delta \omega $ for some $\delta >0$.

A closed real $(1,1)$-current $T$ with $T\geq \delta \omega $ for some $\delta >0$ is called a Kähler current. The cones of pseudo-effective, Kähler, nef and big classes are denoted $\mathcal E$, $\mathcal K$, $\mathcal N$ and $\mathcal B$. The zero class belongs to the pseudo-effective cone and to the nef cone.