Big cone
= Big cone
{title2=$\operatorname{Big}(X)$}
The big cone in $N^1(X)_{\mathbb R}$ is open and convex: write a big class as ample plus effective, perturb only the ample summand, and use openness of the <ample cone>. For positive-dimensional $X$, intersection with $H^{n-1}$ for any very ample divisor $H$ is strictly positive on every big class. Hence this cone contains no line and does not contain the zero class.