Suppose \(X\) is a projective variety of dimension \(n\), and \(D\) is a Cartier divisor on \(X\). Then the line bundle \(\mathcal{O}_X(D)\) is ample if and only if \(\deg D^k\cdot V {\gt} 0\) for every \(k\)-dimensional closed subvariety \(V\) of \(X\).