An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are $674,\!688$ such varieties.

Keywords:

toric, Fano, threefold, canonical singularities, convex polytopes toric, Fano, threefold, canonical singularities, convex polytopes

MSC Classifications:

14J30, 14J30, 14M25, 52B20 show english descriptions $3$-folds [See also 32Q25]
$3$-folds [See also 32Q25]
Toric varieties, Newton polyhedra [See also 52B20]
Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 14J30 - $3$-folds [See also 32Q25]
14J30 - $3$-folds [See also 32Q25]
14M25 - Toric varieties, Newton polyhedra [See also 52B20]
52B20 - Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

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