Deformations and Simultaneous Resolution of Determinantal Surfaces

This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain non-commutative relations, namely those of the canonical algebra of Ringel, are required. All the relations of the reconstruction algebra except the canonical relation are then deformed, and these deformed relations together with variation of the geometric invariant theory (GIT) quotient achieve the simultaneous resolution.