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This is a Quantitative Study study.

October 8, 2025Open Access

Classifying weak Fano toric varieties of Picard rank 3

Key Points

A systematic classification method identifies smooth weak fano toric varieties with Picard rank 3.
In dimension 3, there are 28 isomorphism classes of weak fano toric threefolds.
The classification extends to dimension 4, identifying 114 isomorphism classes of weak fano toric fourfolds.
Macaulay2 is utilized to facilitate the classification of these varieties across dimensions.

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.

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Cite This Study

Hu et al. (Sat,) studied this question.

synapsesocial.com/papers/68e6f342f8145af55aeacabc https://doi.org/https://doi.org/10.48550/arxiv.2506.00715

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