Tohoku Mathematical Journal

Toric varieties whose blow-up at a point is Fano

Laurent Bonavero

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We classify smooth toric Fano varieties of dimension $n\geq 3$ 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 $n\geq 3$ with a fixed point $x\in X$ such that the blow-up $B_x(X)$ 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.

Article information

Tohoku Math. J. (2), Volume 54, Number 4 (2002), 593-597.

First available in Project Euclid: 11 April 2005

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Zentralblatt MATH identifier

Primary: 14J45: Fano varieties
Secondary: 14E30: Minimal model program (Mori theory, extremal rays) 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Toric Fano Varieties blow-up Mori theory


Bonavero, Laurent. Toric varieties whose blow-up at a point is Fano. Tohoku Math. J. (2) 54 (2002), no. 4, 593--597. doi:10.2748/tmj/1113247651.

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