Equations of blowups of ideals of codimension two and three

Access to the defining equations of blowup algebras is a natural pathway to the study of these algebras. In this paper, a generating set is found for the equations of Rees algebras for certain classes of codimension two ideals. From the equations, the Rees algebras are seen to be Cohen-Macaulay. For related classes of codimension three Gorenstein ideals, information is given regarding the degrees of the generators of the ideal of equations. The results depend on the parity of the dimension of the base ring.