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Tohoku Mathematical Journal
2006
March
SECOND SERIES VOL. 58, NO. 1
Tohoku Math. J.
58 (2006), 101121

Title
TORIC FANO THREEFOLDS WITH TERMINAL SINGULARITIES
Author
Alexander M. Kasprzyk
(Received February 13, 2004, revised August 18, 2004) 
Abstract.
This paper classifies all toric Fano 3folds with terminal singularities. This is achieved by solving the equivalent combinatorial problem; that of finding, up to the action of $GL(3,\boldsymbol{Z})$, all convex polytopes in $\boldsymbol{Z}^3$ which contain the origin as the only nonvertex lattice point. We obtain, up to isomorphism, 233 toric Fano 3folds possessing at worst $\boldsymbol{Q}$factorial singularities (of which 18 are known to be smooth) and 401 toric Fano 3folds with terminal singularities that are not $\boldsymbol{Q}$factorial.
2000 Mathematics Subject Classification.
Primary 14J45; Secondary 14J30, 14M25, 52B20.
Key words and phrases.
Toric, Fano, 3folds, terminal singularities, convex polytopes.


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