A canonicity criterion for toric varieties and the classification of canonical 4-simplices

Fuente: arXiv
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Main Author: Ghirlanda, Marco
Format: Preprint
Published: 2026
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author Ghirlanda, Marco
author_facet Ghirlanda, Marco
contents Based on the Reid-Shepherd-Barron-Tai criterion for canonical and terminal quotient singularities, we characterize canonicity and terminality of a toric variety in terms of its local class group actions. Specializing it to the Picard number one setting, we arrive at a classification algorithm for canonical and terminal fake weighted projective spaces in any dimension. In dimension four it gives, up to isomorphism, 710450 canonical fake weighted projective spaces. We take a look at the corresponding Calabi-Yau hypersurfaces, compute the Fine interior of the associated canonical simplices, and discuss the results.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21198
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A canonicity criterion for toric varieties and the classification of canonical 4-simplices
Ghirlanda, Marco
Algebraic Geometry
Combinatorics
14M25, 52B20, 14J32
Based on the Reid-Shepherd-Barron-Tai criterion for canonical and terminal quotient singularities, we characterize canonicity and terminality of a toric variety in terms of its local class group actions. Specializing it to the Picard number one setting, we arrive at a classification algorithm for canonical and terminal fake weighted projective spaces in any dimension. In dimension four it gives, up to isomorphism, 710450 canonical fake weighted projective spaces. We take a look at the corresponding Calabi-Yau hypersurfaces, compute the Fine interior of the associated canonical simplices, and discuss the results.
title A canonicity criterion for toric varieties and the classification of canonical 4-simplices
topic Algebraic Geometry
Combinatorics
14M25, 52B20, 14J32
url https://arxiv.org/abs/2603.21198