On the lengths of quotients of ideals and depths of fiber cones

2009/06/25 by A. V. Jayanthan, Jayanthan, A. V., Ramakrishna Nanduri +1
Mathematics · #13C15 #13H10 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13C15 #msc:13H10

paper · pdf · doi:10.48550/arxiv.0906.4649

16 Pages

arxiv created 2009/06/25 · openalex publication_date 2009/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,\mathfrakm) be a Cohen-Macaulay local ring, I an \mathfrakm-primary ideal of R and J its minimal reduction. We study the depths of F(I) under certain depth assumptions on G(I) and length condition on quotients of powers of I and J, namely ∑_n≥0λ(\mathfrakmIⁿ⁺¹/\mathfrakmJIⁿ) and ∑_n≥0λ(\mathfrakmIⁿ⁺¹ ∩ J/\mathfrakmJIⁿ).

Citations

• Cohen-Macaulay fiber cones

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