Toric varieties whose blow-up at a point is Fano

We classify smooth toric Fano varieties of dimension n greater than or equal to 3 containing a toric divisor isomorphic to the (n - 1)-dimensional projective space. As a consequence of this classification, we show that any smooth complete toric variety X of dimension n greater than or equal to 3 with a fixed point X E X such that the blow-up B., (X) of X at x is Fano is isomorphic either to the n-dimensional projective space or to the blow-up of the n-dimensional projective space along an invariant linear codimension two subspace. As expected, such results are proved using toric Mori theory due to Reid.