# Toward the classification of higher-dimensional toric Fano varieties

@article{Sato1999TowardTC, title={Toward the classification of higher-dimensional toric Fano varieties}, author={Hiroshi Sato}, journal={Tohoku Mathematical Journal}, year={1999}, volume={52}, pages={383-413} }

The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with equivariant blow-ups and blow-downs, and get an easy criterion to determine whether a given nonsingular toric variety is a Fano variety or not. As applications of these results, we get a toric version of a theorem of Mori, and can classify, in principle, all…

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