Cohen-Macaulay local rings with e₂ = e₁-e+1

2020/11/11 by Ankit Mishra, Tony J. Puthenpurakal, Mishra, Ankit +1
Mathematics · #13D45 #13H15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A30 #Secondary 13H10

paper · pdf · doi:10.48550/arxiv.2011.06197

openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study Cohen-Macaulay local rings of dimension d, multiplicity e and second Hilbert coefficient e₂ in the case e₂ = e₁ - e + 1. Let h = μ(\mathfrakm) - d. If e₂ ≠ 0 then in our case we can prove that type A ≥ e - h -1. If type A = e - h -1 then we show that the associated graded ring G(A) is Cohen-Macaulay. In the next case when type A = e - h we determine all possible Hilbert series of A. In this case we show that the Hilbert Series of A completely determines depth G(A).

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