Toric Fano three-folds with terminal singularities
Kasprzyk, Alexander M.
Tohoku Math. J. (2), Tome 58 (2006) no. 1, p. 101-121 / Harvested from Project Euclid
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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.
Publié le : 2006-03-14
Classification:  Toric,  Fano,  $3$-folds,  terminal singularities,  convex polytopes,  14J45,  14J30,  14M25,  52B20 
@article{1145390208,
     author = {Kasprzyk, Alexander M.},
     title = {Toric Fano three-folds with terminal singularities},
     journal = {Tohoku Math. J. (2)},
     volume = {58},
     number = {1},
     year = {2006},
     pages = { 101-121},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1145390208}
}

Kasprzyk, Alexander M. Toric Fano three-folds with terminal singularities. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp.  101-121. http://gdmltest.u-ga.fr/item/1145390208/