Projective Closure of Semigroup Algebras

2024/05/18 by Joydip Saha, Saha, Joydip, Indranath Sengupta +3
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.11319

openalex publication_date 2024/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the projective closure of simplicial affine semigroups in ℕ^d, d ≥ 2. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gröbner bases. Additionally, we establish a criterion, based on Gröbner bases, for determining the Buchsbaum property of non-Cohen-Macaulay projective closures of numerical semigroup rings. Lastly, we introduce the concept of k-lifting for simplicial affine semigroups in ℕ^d, and investigate its relationship with the original simplicial affine semigroup.

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