Quasi-gorensteinness of extended rees algebras

Youngsu Kim, Purdue University

Abstract

Let R be a Noetherian ring and I an R-ideal in Rad(R). It is well known that if the associated graded ring grI ( R) is Cohen-Macaulay or Gorenstein, then so is R. However, the converse does not hold true in general. Therefore, it is interesting to investigate under which conditions good properties of R transfer to gr I (R), or more generally, to Rees algebras. In this thesis, we investigate the Cohen-Macaulayness of gr_I (R) under the assumption that either the extended Rees algebra R[It,t –1] is quasi-Gorenstein, i.e., R[It,t –1] is isomorphic to its graded canonical module, or else grI(R) is an integral domain. We are also able to characterize the Gorensteinness of R[It] via convex geometry when R is a polynomial ring over a field and I is a zero-dimensional monomial ideal.

Degree

Ph.D.

Advisors

Ulrich, Purdue University.

Subject Area

Mathematics

COinS