Toric varieties whose blow-up at a point is Fano

We classify smooth toric Fano varieties of dimension $n\geq 3$ containing a toric divisor isomorphic to \PP^{n-1}. As a consequence of this classification, we show that any smooth complete toric variety $X$ of dimension $n\geq 3$ with a $T$-fixed point $x\in X$ such that the blow-up $B_x(X)$ of $X$ at $x$ is Fano is isomorphic either to \PP^n or to the blow-up of \PP^n along a \PP^{n-2}. As expected, such results are proved using toric Mori theory due to Reid.Comment: 5 pages, no figures. Some mistakes corrected, improvements of presentatio