Local cohomology of multi-Rees algebras, Joint reduction numbers and product of complete ideals
Parangama Sarkar, J. K. Verma
TL;DR
This paper investigates the local cohomology of multi-Rees algebras to predict joint reduction numbers and generalizes a key result on the completeness of power products of complete ideals in unramified local rings.
Contribution
It introduces conditions on local cohomology modules that enable prediction of joint reduction numbers and extends existing results to a broader class of rings.
Findings
Conditions on local cohomology modules for predicting joint reduction numbers
Generalization of Reid-Roberts-Vitulli's result to analytically unramified local rings
Proof of completeness of power products of complete ideals
Abstract
We find conditions on the local cohomology modules of multi-Rees algebras of admissible filtrations which enable us to predict joint reduction numbers. As a consequence we are able to prove a generalisation of a result of Reid-Roberts-Vitulli in the setting of analytically unramified local rings for completeness of power products of complete ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Polynomial and algebraic computation