Bigraded structures and the depth of blow-up algebras

2004/05/18 by Juan Elías, Elias, Juan, Gemma Colomé-Nin +1
Mathematics · #13A30 #13C14 #13D40 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0405344

openalex publication_date 2004/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Cohen-Macaulay local ring, and let I⊂ R be an ideal with minimal reduction J. In this paper we attach to the pair I, J a non-standard bigraded module Σ^I,J. The study of the bigraded Hilbert function of \SIJ allows us to prove a improved version of Wang's conjecture and a weak version of Sally's conjecture, both on the depth of the associated graded ring gr_I(R). The module \SIJ can be considered as a refinement of the Sally's module previously introduced by W. Vasconcelos.

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• On the depth of blow-up rings of ideals of minimal mixed multiplicity
• Relative Cohen--Macaulayness of bigraded modules
• Sally modules and associated graded rings
• On the diagonals of a Rees algebra