Geodesic
A note on the smooth blowups of $\mathbb {P}(1,1,1,k)$ in torus-invariant subvarieties
Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1152-1163

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This papers classifies toric Fano threefolds with singular locus $\{ \frac {1}{k}(1,1,1) \}$ for $k \in \mathbb {Z}_{\geq 1}$ building on the work of Batyrev (1981, Nauk SSSR Ser. Mat. 45, 704–717) and Watanabe–Watanabe (1982, Tokyo J. Math. 5, 37–48). 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 $k \geq 4$, there are exactly two such toric Fano threefolds linked by a blowup in a torus-invariant line.
DOI : 10.4153/S0008439523000231
Mots-clés : Fano threefolds, cascades, Fano polytopes, cyclic quotient singularities 
Cavey, Daniel. A note on the smooth blowups of $\mathbb {P}(1,1,1,k)$ in torus-invariant subvarieties. Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1152-1163. doi: 10.4153/S0008439523000231
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     title = {A note on the smooth blowups of $\mathbb {P}(1,1,1,k)$ in torus-invariant subvarieties},
     journal = {Canadian mathematical bulletin},
     pages = {1152--1163},
     year = {2023},
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