Multipointed NC deformations and CY3folds

I will consider non-commutative deformation functor from the category of r-pointed Artin algebras to the category of sets arising from a simple collection of sheaves on a variety. If the variety is a 3-dimensional local Calabi–Yau manifold near the supports of the sheaves, then we prove that the semi-universal family becomes a relative spherical object over the deformation ring and gives a spherical twist of the derived category if the deformation stops after finitely many iterated extensions. We also consider a generalization in the case of Calabi–Yau category.