= Ample divisor after blowing up a torus-fixed point
{title2=$c\pi^*D-E$}
For an ample invariant divisor $D$ and the blowup $\pi$ of a torus-fixed smooth point in dimension at least two, $c\pi^*D-E$ is ample for sufficiently large integers $c$. In the subdivided cone, its local characters are $cm_\sigma+u_i$, where $u_i$ is dual to the omitted ray generator. The new strict inequalities have gap one on the omitted ray and grow linearly with $c$ elsewhere, proving the claim by the <toric ampleness criterion>.
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