The Gorenstein and complete intersection properties of associated graded rings

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• 作者：William Heinzer ; Mee-Kyoung Kim and Bernd Ulrich
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2005
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：2005
• 卷：201
• 期：1-3
• 页码：264-283
• 文件大小：294 K

摘要

Let I be an -primary ideal of a Noetherian local ring . 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 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 complete intersection. In case is Gorenstein, we give a necessary and sufficient condition for 16016f6c08435ac539449a02c5" title="Click to view the MathML source">G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with μ(J)=dimR and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein if and only if for 0ir-1. If is a Gorenstein local ring and 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 for every . If, in addition, dimR