PomeCorollary 21.13.10.0D3DB05576E8 The stable 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 elements in $\Sigma $ satisfying (21.13.9) for each $m\in P_ D$.
Corollary 21.13.100D3DB05576E8
Proof. It follows from proposition 21.13.8 that the stable base locus of $D$ is given by the union of the $V(\tau )$'s, where $\tau $ runs over elements of $\Sigma $ satisfying (21.13.9) for all $m\in M_{\mathbb {Q}}\cap P_ D$. That is,
\[ M_{\mathbb {Q}}\cap \left\{ m\in P_ D : a_{\rho }+\langle m, u_{\rho }\rangle =0\quad \forall \rho \in \tau (1) \right\} =\varnothing . \]
Since the latter part is a rational polytope, this statement is equivalent to
7480F81CDDBD
21.13.11
\begin{equation} \left\{ m\in P_ D : a_{\rho }+\langle m, u_{\rho }\rangle =0\quad \forall \rho \in \tau (1) \right\} =\varnothing . \end{equation}
Our first assertion follows. $\square$
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