
TL;DR
This paper develops methods to compute multiplier modules for extended Rees algebras of ideals in local rings, providing decomposition theorems that relate these modules to properties like rational singularities.
Contribution
It introduces a decomposition theorem for multiplier modules of extended Rees algebras, enabling explicit calculations and insights into their singularity properties.
Findings
Decomposition theorem for multiplier modules of extended Rees algebras
Explicit computation methods for multiplier modules of Rees and extended Rees algebras
Connections established between multiplier modules and rational singularities
Abstract
Given a local ring and an ideal of positive height, we give a way of computing multiplier module for the extended Rees algebra for an ideal by proving a decomposition theorem for , (also see the works of Budur, Musta\c{t}\u{a} and Saito). We compute the multiplier module for the Rees algebra as well (also see the works of Hyry and Kotal-Kummini). We use these decompositions to understand relationships between associated graded rings, Rees and extended Rees algebras having rational singularities (also see the works of Hara, Watanabe, and Yoshida).
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