A variation of an algebra A is essentially a representation of A as a quotient of a fixed algebra R by an ideal I(\lambda) which depends on some parameter(s). The problem is to determine when this is actually a deformation of A, since the ideal may "jump" when the parameter is varied. In the special case where the dependence is (in a natural sense) rational then the use of a Groebner basis shows that one can find a fixed subspace M of R which will serve as a complement to I(\lambda) for all but a finite number of values of \lambda. Therefore, if one starts at a value of \lambda which is not one of these exceptional values then a small change in \lambda does give a deformation. An open problem is to find the infinitesimal of this deformation (in the classical sense). [If time permits I will also give a short addendum to Tony Giaquinto's talk of last week.]