Lemma A.3 . [01CS]

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Lemma A.3.

With the previous notation let $\theta\in\mathcal{Z}^{1,1}(X)$ be the curvature form of the model metric induced by $\mathcal{L}$ . Then $(\theta,0)$ satisfies (A.1) iff the approximate Zariski decompositions (A.2) are asymptotically orthogonal, in the sense that

(A.3)

\lim_{m\to\infty}\left(\tfrac{1}{m}\mathcal{M}_{m}\right)^{n}\cdot\left(\tfrac{1}{m}F_{m}\right)=0.