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Bigraded structures and the depth of blow-up algebras | | Juan Elias
; Gemma Colomé-Nin
; | | Date: |
18 May 2004 | | Subject: | Commutative Algebra MSC-class: 13A30; 13C14; 13D40 | math.AC | | Abstract: | Let $R$ be a Cohen-Macaulay local ring, and let $Isubset R$ be an ideal with minimal reduction $J$. In this paper we attach to the pair $I$, $J$ a non-standard bigraded module $Sigma^{I,J}$. 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. | | Source: | arXiv, math.AC/0405344 | | Services: | Forum | Review | PDF | Favorites | |
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