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2006 Toric Fano three-folds with terminal singularities
Alexander M. Kasprzyk
Tohoku Math. J. (2) 58(1): 101-121 (2006). DOI: 10.2748/tmj/1145390208

Abstract

This paper classifies all toric Fano $3$-folds with terminal singularities. This is achieved by solving the equivalent combinatorial problem; that of finding, up to the action of $GL(3,\Z)$, all convex polytopes in $\Z^3$ which contain the origin as the only non-vertex lattice point. We obtain, up to isomorphism, $233$ toric Fano $3$-folds possessing at worst $\Q$-factorial singularities (of which $18$ are known to besmooth) and $401$ toric Fano $3$-folds with terminal singularities that are not $\Q$-factorial.

Citation

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Alexander M. Kasprzyk. "Toric Fano three-folds with terminal singularities." Tohoku Math. J. (2) 58 (1) 101 - 121, 2006. https://doi.org/10.2748/tmj/1145390208

Information

Published: 2006
First available in Project Euclid: 18 April 2006

zbMATH: 1118.14047
MathSciNet: MR2221794
Digital Object Identifier: 10.2748/tmj/1145390208

Subjects:
Primary: 14J45
Secondary: 14J30, 14M25, 52B20

Rights: Copyright © 2006 Tohoku University

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Vol.58 • No. 1 • 2006
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