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2009 Algorithms for Projectivity and Extremal Classes of a Smooth Toric Variety
Anna Scaramuzza
Experiment. Math. 18(1): 71-84 (2009).


In this paper we present two algorithms: the first tests the projectivity of a smooth complete toric variety and the second determines the extremal classes of the Mori cone of a smooth projective toric variety. The crucial fact is that we are able to give a complete description of $\aunox$, determining a basis $B$ of $\aunox$ and the coordinates with respect to $B$ of any element of $\aunox$. The computational condition testing the projectivity is obtained by Kleiman's criterion of ampleness, while the condition determining the extremality of a class comes directly from the definition of a nonextremal class. The algorithms are used to study the Mori cone of Fano toric $n$-folds with dimension $n\leq 4$ and Picard number $\rho \geq 3$, computing all extremal rays of the Mori cone. Moreover, we describe a toric almost Fano variety of dimension $3$ and Picard number $35$ together with its Mori cone.


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Anna Scaramuzza. "Algorithms for Projectivity and Extremal Classes of a Smooth Toric Variety." Experiment. Math. 18 (1) 71 - 84, 2009.


Published: 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1169.14009
MathSciNet: MR2548988

Primary: 13P10 , 14E30 , 14M25

Keywords: algorithms , extremal classes , projectivity , toric varieties

Rights: Copyright © 2009 A K Peters, Ltd.


Vol.18 • No. 1 • 2009
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