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# Canonical Toric Fano Threefolds

Published:2010-08-18
Printed: Dec 2010
• Alexander M. Kasprzyk,
School of Mathematics and Statistics, University of Sydney, Sydney, Australia
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## Abstract

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
 MSC Classifications: 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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