Toric Fano 3-folds with terminal singularities

Abstract

This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric 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.

19 pages

References in corpus (3)

• On Fano indicies of Q-Fano 3-folds
• Resolving 3-dimensional toric singularities
• Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint

Cited by in corpus (21)

• Canonical toric Fano threefolds
• Bounds on Fake Weighted Projective Space
• Effective action from M-theory on twisted connected sum $G_2$-manifolds
• On terminal Fano 3-folds with 2-torus action
• Lattice 3-polytopes with six lattice points
• Smooth Fano polytopes arising from finite directed graphs
• Lattice 3-polytopes with few lattice points
• Fano threefolds as equivariant compactifications of the vector group
• Few smooth d-polytopes with n lattice points
• On deformations of toric Fano varieties
• Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
• Minkowski length of 3D lattice polytopes
• On the anticanonical complex
• The anticanonical complex for non-degenerate toric complete intersections
• Toric $G$-Fano Threefolds
• On Fano threefolds with ${\mathbb{C}}^{\ast }$-action
• Sharp bounds on fake weighted projective spaces with canonical singularities
• On terminal Fano 3-folds with 2-torus action, part II
• Classification of width 1 lattice tetrahedra by their multi-width
• Terminal toric Fano three-folds with certain numerical conditions
• A note on the smooth blow-ups of P(1,1,1,k) in torus-invariant subvarieties