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.