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Is there a classification of complex Fano $3$-folds, with Picard rank $1$ and a single cyclic quotient singularity of type $\frac{1}{2}(1,1,1)$?

This should be a bounded family by a result of Borisov.

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    $\begingroup$ I'm not sure if a nice clean statement exists, but this paper of Takagi at least covers some of the classification you hope for projecteuclid.org/download/pdf_1/euclid.nmj/1114649295 $\endgroup$
    – Tom Ducat
    Commented Mar 24, 2020 at 12:01
  • $\begingroup$ Is it a fact that such Fano 3-folds are not smoothable? $\endgroup$
    – Evgeny Shinder
    Commented Mar 26, 2020 at 17:25
  • $\begingroup$ Yes, they are not smoothable. Indeed the singularity 1/2(1,1,1) is rigid (i.e. it doesn't deform) - see Schlessinger's "Rigidity of quotient singularities", Invent. math., vol. 14, pages 17-26 (1971). $\endgroup$
    – Andrea
    Commented Jan 11, 2021 at 10:02

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