Gorensteinness in Rees algebras of powers of parameter ideals

2021/12/13 by Goto, Shiro, Iai, Shin-ichiro
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.06676

Abstract

This paper gives a necessary and sufficient condition for Gorensteinness in Rees algebras of the d-th power of parameter ideals in certain Noetherian local rings of dimension d≥ 2. The main result of this paper produces many Gorenstein Rees algebras over non-Cohen-Macaulay local rings. For example, the Rees algebra R(\mathfrakq^d)=⊕_{i≥ 0}\mathfrakq^di is Gorenstein for every parameter ideal \mathfrakq that is a reduction of the maximal ideal in a d-dimensional Buchsbaum local ring of depth 1 and multiplicity 2.

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• When are the rings I:I Gorenstein?
• Almost Gorenstein Rees algebras of p_g-ideals, good ideals, and powers of the maximal ideals
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