Classifying weak Fano toric varieties of Picard rank $3$

Q: What type of study is this?

This is a Quantitative Study study.

Zhengning Hu; R. K. SAXENA V. G. JOSHI

doi:10.48550/arxiv.2506.00715

May 31, 2025Open Access

Classifying weak Fano toric varieties of Picard rank $3$

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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.

Implication

Systematic method classifies weak Fano toric varieties in any dimension, revealing 28 classes in threefolds and 114 in fourfolds.

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. (2025) studied this question.

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

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Classifying weak Fano toric varieties of Picard rank $3$

Key Points

Implication

Abstract

Discussion

Cite This Study

Classifying weak Fano toric varieties of Picard rank $3$

Key Points

Implication

Abstract

Discussion

Cite This Study

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