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arXiv · 2405.11319

Projective Closure of Semigroup Algebras

Joydip Saha·Indranath Sengupta·Pranjal Srivastava
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Abstract

This paper investigates the projective closure of simplicial affine semigroups in $\mathbb{N}^{d}$, $d \geq 2$. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gr\"{o}bner bases. Additionally, we establish a criterion, based on Gr\"{o}bner 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 $\mathbb{N}^d$, and investigate its relationship with the original simplicial affine semigroup.

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Joydip Saha, Indranath Sengupta, Pranjal Srivastava. 2024-05-18. Projective Closure of Semigroup Algebras. https://arxiv.org/abs/2405.11319

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