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2002 Toric varieties whose blow-up at a point is Fano
Laurent Bonavero
Tohoku Math. J. (2) 54(4): 593-597 (2002). DOI: 10.2748/tmj/1113247651

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.

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Laurent Bonavero. "Toric varieties whose blow-up at a point is Fano." Tohoku Math. J. (2) 54 (4) 593 - 597, 2002. https://doi.org/10.2748/tmj/1113247651

Information

Published: 2002
First available in Project Euclid: 11 April 2005

zbMATH: 1021.14014
MathSciNet: MR1936270
Digital Object Identifier: 10.2748/tmj/1113247651

Subjects:
Primary: 14J45
Secondary: 14E30, 14M25

Rights: Copyright © 2002 Tohoku University

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Vol.54 • No. 4 • 2002
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