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On the classification of toric Fano 4-folds

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Abstract

The biregular classification of smoothd-dimensional toric Fano varieties is equivalent to the classification of special simplicial polyhedraP in ℝd, the so-called Fano polyhedra, up to an isomorphism of the standard lattice\(\mathbb{Z}^d \subset \mathbb{R}^d\). In this paper, we explain the complete biregular classification of all 4-dimensional smooth toric Fano varieties. The main result states that there exist exactly 123 different types of toric Fano 4-folds somorphism.

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  1. V. V. Batyrev
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory Vol. 56. Algebraic Geometry-9, 1998.

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Batyrev, V.V. On the classification of toric Fano 4-folds. J Math Sci 94, 1021–1050 (1999). https://doi.org/10.1007/BF02367245

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