Toric Fano three-folds with terminal singularities
Alexander M. Kasprzyk
Source: Tohoku Math. J. (2) Volume 58, Number 1
(2006), 101-121.
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 be smooth) and $401$ toric Fano $3$-folds with terminal singularities that are not $\Q$-factorial.
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Permanent link to this document: http://projecteuclid.org/euclid.tmj/1145390208
Digital Object Identifier: doi:10.2748/tmj/1145390208
Mathematical Reviews number (MathSciNet): MR2221794
Zentralblatt MATH identifier: 1118.14047
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