= Uniform ample subtraction from a big divisor with ample exceptional restrictions
{title2=$D-\epsilon A\text{ is nef}\quad(0<\epsilon\ll1)$}
If a big class $D=B+E$ has <ample> restriction to every component $E_i$ of the effective support, then for any <ample> $A$ a sufficiently small $\epsilon>0$ makes $D-\epsilon A$ <nef>. Use openness of the <ample cone> to keep $B-\epsilon A$ and all $(D-\epsilon A)|_{E_i}$ <ample> with one finite minimum of bounds. Curves inside the support use these restrictions; curves outside use effectivity of $E$. Thus one does not need a uniform choice over infinitely many <subvarieties>.
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