Take care of non-principal exceptional divisors.

experimental/Schemes/src/BlowupMorphism.jl

@@ -644,18 +644,18 @@ function produce_object_on_affine_chart(I::StrictTransformIdealSheaf, U::AbsAffi
  f_loc = covering_morphism(f)[U]
  V = codomain(f_loc)
  IE_loc = IE(U)
- @assert isone(ngens(IE_loc)) "ideal sheaf of exceptional locus is not principal"
- tot = pullback(f_loc)(J(V))
- #return saturation_with_index(tot, IE_loc)
  # It is usually better to pass to the simplified covering to do the computations
  simp_cov = simplified_covering(X)
  U_simp = first([V for V in patches(simp_cov) if original(V) === U])
  a, b = identification_maps(U_simp)
- # This used to be the following line. But we don't use the index, so we 
- # switch to the more performant version
- # result, _ = saturation_with_index(pullback(a)(tot), pullback(a)(IE_loc))
- result = _iterative_saturation(pullback(a)(tot), elem_type(OO(U_simp))[pullback(a)(u) for (u, _) in factor(lifted_numerator(first(gens(IE_loc))))])
- return pullback(b)(result)
+ tot = pullback(f_loc)(J(V))
+ if isone(ngens(IE_loc))
+ result = _iterative_saturation(pullback(a)(tot), elem_type(OO(U_simp))[pullback(a)(u) for (u, _) in factor(lifted_numerator(first(gens(IE_loc))))])
+ return pullback(b)(result)
+ else
+ result, _ = saturation_with_index(pullback(a)(tot), pullback(a)(IE_loc))
+ return result
+ end
 end
 
 @attr Bool function is_prime(I::StrictTransformIdealSheaf)