an isomorphism? These questions have interest partly because if S and .S’(J, S) are Cohen-Macaulay, then so is gr, S := S/J@ J/J’... [ 16 1 and under these hypotheses if N is perfect and R @ .S(J, S) = .$(I, R), then R and .7(1. R) are Cohen-Macaulay too. Thus, gr,R is Cohen-Macaulay, and its torsion freeness and normality, for exmple, can be characterized in terms of analytic spreads, as in [ ...

We prove that a Cohen-Macaulay normal variety X has Du Bois singularities if and only if π∗ωX′(G) ≃ ωX for a log resolution π : X ′ → X , where G is the reduced exceptional divisor of π. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward an...

If V is an equidimensional codimension c subscheme of an n-dimensional projective space, and V is linked to V ′ by a complete intersection X, then we say that V is minimally linked to V ′ if X is a codimension c complete intersection of smallest degree containing V . Gaeta showed that if V is any arithmetically Cohen-Macaulay (ACM) subscheme of codimension two then there is a finite sequence of...