All smooth weak Fano toric threefolds and fourfolds of Picard rank 3 are classified, with 28 and 114 isomorphism classes, and a cohomological converse to Bott-Steenbrink-Danilov vanishing is proved.
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Classifying weak Fano toric varieties of Picard rank $3$
All smooth weak Fano toric threefolds and fourfolds of Picard rank 3 are classified, with 28 and 114 isomorphism classes, and a cohomological converse to Bott-Steenbrink-Danilov vanishing is proved.