Tohoku Mathematical Journal
2006
March
SECOND SERIES VOL. 58, NO. 1

Tohoku Math. J.
58 (2006), 101-121

Title TORIC FANO THREE-FOLDS WITH TERMINAL SINGULARITIES

Author Alexander M. Kasprzyk

(Received February 13, 2004, revised August 18, 2004)
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 $GL(3,\boldsymbol{Z})$, all convex polytopes in $\boldsymbol{Z}^3$ which contain the origin as the only non-vertex lattice point. We obtain, up to isomorphism, 233 toric Fano 3-folds possessing at worst $\boldsymbol{Q}$-factorial singularities (of which 18 are known to be smooth) and 401 toric Fano 3-folds 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, 3-folds, terminal singularities, convex polytopes.

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