Local Cohomology of Multi-Rees Algebras with Applications to Joint Reductions and Complete Ideals

2014/07/06 by Shreedevi K. Masuti, Tony J. Puthenpurakal, Masuti, Shreedevi K. +3
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.1493

openalex publication_date 2014/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a generalization, in dimension 3, of a theorem of David Rees about joint reductions of the bigraded filtration \ I^rJ^s\ of complete \mathfrak m-primary ideals and vanishing of the second normal Hilbert coefficient e₂(IJ) where R is a two-dimensional Cohen-Macaulay analytically unramified local ring with maximal ideal \mathfrak m. This generalization is obtained as a consequence of a formula for the third local cohomology module of the extended Rees algebras of the \mathbb Z³-graded filtration \I^rJ^sK^t\ with support in the ideal (x₁t₁,x₂t₂,x₃t₃) where (x₁,x₂,x₃) is a good joint reduction of \I^rJ^sK^t\.

Related

• Local cohomology of multi-Rees algebras, Joint reduction numbers and product of complete ideals
• Local Cohomology of Bigraded Rees Algebras and Normal Hilbert Coefficients
• An extension of Rees theorem and two interpretations of a vector in the joint reduction lattice
• On Coefficient ideals
• Postulation and reduction vectors of multigraded filtrations of ideals