Consider a singular curve Γ contained in a smooth 3-fold X. Assuming the general elephant conjecture, the general hypersurface section Γ⊂S⊂X is Du Val. Under that assumption, this paper describes the construction of a divisorial extraction from Γ by Kustin–Miller unprojection. Terminal extractions from Γ⊂X are proved not to exist if S is of type D2k,E7 or E8 and are classified if S is of type A1,A2 or E6.
- Divisorial extractions