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Bigraded structures and the depth of blow-up algebras

Juan Elias·Gemma Colomé-Nin
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Abstract

Let $R$ be a Cohen-Macaulay local ring, and let $I\subset R$ 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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Juan Elias, Gemma Colomé-Nin. 2006-10-02. Bigraded structures and the depth of blow-up algebras. https://arxiv.org/abs/math/0405344

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