0 Se p 20 07 Structure theorems for certain Gorenstein ideals . ∗

Let d = dim(A) be the dimension, e the multiplicity and h = v(m)−d the embedding codimension of A. We assume that k is a characteristic zero field (see the comment after Proposition 2.3). A classical problem in the theory of local rings is the determination of the minimal number of generators v(I) := dimk(I/nI) of the ideal I under certain restrictions on the numerical characters of A. For example, by a classical theorem of Abhyankar, we know that e ≥ h+1, and if the equality e = h+1 holds we say that A has minimal multiplicity and we know that v(I) = (