Classifying weak Fano toric varieties of Picard rank 3

2025/05/31 by Zhengning Hu, Hu, Zhengning, Rohan Joshi +1
Mathematics · #14-04 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.00715

openalex publication_date 2025/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a systematic method to classify all smooth weak Fano toric varieties of Picard rank 3 in any dimension using Macaulay2, and describe the classification explicitly in dimensions 3 and 4. There are 28 and 114 isomorphism classes of rank 3 weak Fano toric threefolds and fourfolds, respectively.

Citations

• An Update on the Classification of Rank 2 Weak Fano Threefolds
• A sufficient condition for a toric weak Fano 4-fold to be deformed to a Fano manifold
• An algorithm for the classification of smooth Fano polytopes
• Cohomology of rational forms and a vanishing theorem on toric varieties
• The classification of smooth toric weakened Fano 3-folds
• Toward the classification of higher-dimensional toric Fano varieties

Related

• Images of toric variety and amplified endomorphism of weak Fano threefolds
• An Update on the Classification of Rank 2 Weak Fano Threefolds
• Bounds on the Picard rank of toric Fano varieties with minimal curve constraints
• The classification of smooth toric weakened Fano 3-folds
• Rank two Weak Fano bundles on Fano threefolds of Picard rank one