Let $X$ be a complex, projective, nonsingular variety. We also understand it as a Kähler Manifold. My question now is, when people say $c_1(X) < 0$, what exactly do they mean? Let me elaborate. In this paper, it is said that Yau's inequality

$$ (-1)^n c_1^n \le (-1)^n \frac{2(n+1)}{n} c_2 c_1^{n-2} $$

holds under the condition that $c_1(X) < 0$. I would have thought that this is equivalent to $K_X$ being effective. In the original paper, Yau requires $X$ to have **ample** canonical class, however. Now, I am wondering: For the above equality to hold, do I need $K_X$ to be ample or does it suffice for $K_X$ to be effective?