Toric varieties whose blow-up at a point is Fano

الأصل · EN

We classify smooth toric Fano varieties of dimension n≥ 3 containing a toric divisor isomorphic to ⁿ⁻¹. As a consequence of this classification, we show that any smooth complete toric variety X of dimension n≥ 3 with a T-fixed point x∈ X such that the blow-up Bₓ(X) of X at x is Fano is isomorphic either to ⁿ or to the blow-up of ⁿ along a ⁿ⁻². As expected, such results are proved using toric Mori theory due to Reid.