Jan O. Kleppe
The purpose of this paper is to study maximal irreducible families of (e.g. Artinian) Gorenstein quotients of a polynomial ring R. If GradAlg^H(R) is the scheme parametrizing graded quotients of R with Hilbert function H, we prove there is a close relationship between the generically smooth irreducible components of GradAlg^H(R) whose general member is a Gorenstein codimension (c+1) quotient, and the generically smooth irreducible components of GradAlg^{H'}(R) whose general member B is a codimension c Cohen-Macaulay algebra. Moreover the dimension of the ``Gorenstein'' components are computed in terms of the dimension of the corresponding ``Cohen-Macaulay'' component and of other invariants of B. Furthermore we show that linkage is quite effective in computing all invariants of the dimension formula as well as verifying the assumptions which appears in a generalization of the main Theorem.