Tohoku Mathematical Journal

Toric varieties whose blow-up at a point is Fano

Laurent Bonavero

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Abstract

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

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

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247651

Digital Object Identifier
doi:10.2748/tmj/1113247651

Mathematical Reviews number (MathSciNet)
MR1936270

Zentralblatt MATH identifier
1021.14014

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

Keywords
Toric Fano Varieties blow-up Mori theory

Citation

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. https://projecteuclid.org/euclid.tmj/1113247651


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References

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