= Componentwise bigness on a projective scheme
For a possibly reducible <projective scheme>, componentwise bigness means that a real Cartier class restricts to a <big real divisor> on every reduced irreducible component. This specifies the convention needed by positivity arguments that treat all curves. Maximal total section growth alone is weaker: on $\mathbb P^2\amalg\mathbb P^2$, the bundle $(\mathcal O(1),\mathcal O(-1))$ has quadratic total growth but negative degree on every line in the second component. Thus its negative curves cannot be confined to finitely many divisors.
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