The Gorenstein and complete intersection properties of associated graded rings
| dc.creator | Heinzer, William | |
| dc.creator | Kim, Mee-Kyoung | |
| dc.creator | Ulrich, Bernd | |
| dc.date | 2004-06-06 | |
| dc.date | 2005-02-25 | |
| dc.date.accessioned | 2026-07-07T05:08:54Z | |
| dc.date.available | 2026-07-07T05:08:54Z | |
| dc.description | Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F(I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I, we observe that: (i) G(I) is Cohen-Macaulay iff F(I) is Cohen- Macaulay, (ii) G(I) is Gorenstein iff both F(I) and R/I are Gorenstein, and (iii) G(I) is a relative complete intersection iff F(I) is a relative complete intersection. In case R/I is Gorenstein, we give a necessary and sufficient condition for G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with μ(J) = dim R and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein iff J:I^{r-i} = J + I^{i+1}, for i = 0, ...,r-1. If (R,m) is a Gorenstein local ring and I \subseteq m is an ideal having a reduction J with reduction number r such that μ(J) = ht(I) = g > 0, we prove that the extended Rees algebra R[It, t^-1}] is quasi-Gorenstein with \a-invariant a if and only if J^n:I^r = I^{n+a-r+g-1} for every integer n. | |
| dc.identifier | https://arxiv.org/abs/math/0406097 | |
| dc.identifier | http://arxiv.org/abs/math/0406097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71446 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A30 | |
| dc.title | The Gorenstein and complete intersection properties of associated graded rings | |
| dc.type | text |