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Sharp Bounds and Canonical Blow-ups for Toric Projectivization
For every dimension $n\ge3$, we construct a family $Σ_n(a,b)$ of smooth complete fans with Picard number five and fixed combinatorial type. For integers $a,b\ge1$, the minimum number of new rays in a smooth projective refinement is $\min(a,b)$, attained by ordinary invariant codimension-two blow-ups
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