A note on the smooth blow-ups of P(1,1,1,k) in torus-invariant subvarieties

2020/09/06 by Cavey, Daniel
#14J45 (Secondary) #14M25 (Primary) 14J30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.02746

Abstract

This paper classifies toric Fano 3-folds with singular locus 1/k(1,1,1) for any positive integer k, building on the work of Batyrev and Watanabe-Watanabe. This is achieved by completing an equivalent problem in the language of Fano polytopes. Furthermore we identify birational relationships between entries of the classification. For a fixed value k>4, there are exactly two such Fano 3-folds linked by a blow-up in a torus-invariant line.

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