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Corollary 21.13.819B7387A93262

Corollary 21.13.81.9B7387A93262 The augmented base locus (with the reduced complex structure) of $D$ is a toric-invariant (possibly reducible) subvariety given by the union of the $V(\tau )$'s, where $\tau $ runs over the elements in $\Sigma $ such that

\[ \dim Q_{\tau }<n-\dim \tau {}^{\href{#sgpt-a0000106136}{6}}. \]

Proof. Apply corollary 21.13.79 to $\varphi =V_{\theta }$. Together with Nakamaye's theorem [Theorem 5.7, ELMNP09] and theorem 20.2.34, this says that $V(\tau )$ lies in the augmented base locus exactly when the $\dim V(\tau )$-dimensional volume of $Q_{\tau }$ is zero, which is equivalent to $\dim Q_{\tau }<n-\dim \tau $. $\square$

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