REGULARITY OF REES ALGEBRAS

Abstract

Let B = k[x1, …, xn] be a polynomial ring over a field k, and let A be a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[m t] also has a presentation as a quotient ring of the polynomial ring k[x1, …, xn, y1, …, yn] by a homogeneous ideal J*. For instance, if A = k[x1, …, xn],\sthen R≅k[x1,…,xn,y1,…,yn]/(xiyj−xjyi|i, j=1,…,n). In this paper we want to compare the homological properties of the homogeneous ideals J and J*.