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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In particular, they give rise to squarefree initial ideals as well.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities.
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Key Findings & Data:We compute explicit Gröbner bases for these toric ideals that are also minimal generating sets consisting of large number of binomials of degree ≤ 4.
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Conclusion & Impact:In particular, they give rise to squarefree initial ideals as well.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:toric ideals · simple surface singularities · semigroup of Lipman
Abstract
In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gröbner bases for these toric ideals that are also minimal generating sets consisting of large number of binomials of degree ≤ 4. In particular, they give rise to squarefree initial ideals as well.
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Cite This Article
ŞAHİN, M., METE, P., KAYA, G. (2022). Toric ideals of simple surface singularities. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 5, 1057–1069. https://ajindex.com/articles/530310