Canonical toric Fano threefolds

Abstract

An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.

21 pages, 1 figure

References in corpus (3)

• Gorenstein toric Fano varieties
• An algorithm for the classification of smooth Fano polytopes
• Bounds on Fake Weighted Projective Space

Cited by in corpus (40)

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• Smooth Fano polytopes arising from finite directed graphs
• Mutations of fake weighted projective planes
• Enumeration of lattice 3-polytopes by their number of lattice points
• Few smooth d-polytopes with n lattice points
• Degenerations to Unobstructed Fano Stanley-Reisner Schemes
• On toric geometry and K-stability of Fano varieties
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• Classifying terminal weighted projective space
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• Reflexive polytopes of higher index and the number 12
• Polytopes and Machine Learning
• Relative Algebro-Geometric stabilities of Toric Manifolds
• Three-dimensional lattice polytopes with two interior lattice points
• On the anticanonical complex
• On the Fine Interior of Three-dimensional Canonical Fano Polytopes
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• Mutations of Fake Weighted Projective Spaces
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• The anticanonical complex for non-degenerate toric complete intersections
• The covering radius and a discrete surface area for non-hollow simplices
• The Finiteness Threshold Width of Lattice Polytopes
• Stringy $E$-functions of canonical toric Fano threefolds and their applications
• On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces
• On Fano threefolds with ${\mathbb{C}}^{\ast }$-action
• Asymptotic Chow semistability implies Ding polystability for Gorenstein toric Fano varieties
• Sharp bounds on fake weighted projective spaces with canonical singularities
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• On the resolution of constant scalar curvature Kähler orbifolds
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• Separation of integer points by a hyperplane under some weak notions of discrete convexity
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• On terminal Fano 3-folds with 2-torus action, part II
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• Smooth Fano polytopes arising from finite partially ordered sets
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