The classification of toric canonical Fano 3-folds

Description

The classification of toric canonical Fano 3-folds This dataset describes the classification of all toric canonical Fano 3-folds [1]. Equivalently, it describes the classification of all 3-dimensional convex lattice polytopes with exactly one interior lattice point. A toric Fano 3-fold \(X\) (that is, a 3-dimensional toric variety with ample anticanonical divisor \(-K\) ) with at worst canonical singularities corresponds to a 3-dimensional convex polytope \(P\) with vertices that are primitive integer vectors, and such that \(P\) contains exactly one lattice point, the origin, in its strict interior. The fan of \(X\) is given by the spanning fan of \(P\) : that is, the fan whose cones are spanned by the faces of \(P\) . In the language of toric geometry, \(P\) is in the lattice \(N \cong \mathbb{Z}^3\) . Since two polytopes which are equal after a lattice change of basis give rise to isomorphic toric varieties, a polytope is regarded as being defined only up to the action of \(\mathrm{GL}(\mathbb{Z}^3)\) . There are 674688 isomorphism classes. For details, see the paper [1]. If you make use of this data, please consider citing [1] and the DOI for this data…

Description from Zenodo, shortened.

Files (4)

• TXTREADME.txt8.2 kB
• TXTtoricf3c.txt779 MB
• SQLtoricf3c.sql538 MB
• —LICENSE6.9 kB

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