Abstract:
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.
