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Journal of the London Mathematical Society 2002 65(2):320-338; doi:10.1112/S0024610701002794
© 2002 by London Mathematical Society
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© The London Mathematical Society

Regularity of Rees Algebras

Jürgen Herzog, Dorin Popescu and Ngô Viêt Trung

Fachbereich Mathematik, Universität-GHS Essen 45117 Essen, Germany, juergen.herzog{at}uni-essen.de
Institute of Mathematics, University of Bucharest PO Box 1-764, Bucharest 70700, Romania, dorin{at}stoilow.imar.ro
Institute of Mathematics Box 631, Bò Hô, 10000 Hanoi, Vietnam, nvtrung{at}thevinh.ncst.ac.vn

Received 2 October 2000. Revision received 9 May 2001.

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], then

R{cong}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*.


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