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Feb 6, 2019 at 3:38 answer added Sándor Kovács timeline score: 2
Feb 4, 2019 at 8:07 comment added Tom Ducat The singularity you describe is case 4 of Theorem 9.6 in Kawamata's paper "Crepant Blowing-Up of 3-Dimensional Canonical Singularities and Its Application to Degenerations of Surfaces". In the proof he explains how it is obtained it as a Z/2-quotient of a cusp singularity. If by 'construct' you mean 'write down equations for' then that is probably much harder.
Feb 4, 2019 at 1:16 history asked xin fu CC BY-SA 4.0