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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
📌 3 Key Takeaways
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Objective & Hypothesis:We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space.
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Key Findings & Data:We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangentcone has fiveminimal generators and showthat the possible Betti sequences are (1,5,6,2) and (1,5,5,1).
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Conclusion & Impact:Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Gorenstein monomial curves · tangent cones · minimal free resolutions
Abstract
We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangentcone has fiveminimal generators and showthat the possible Betti sequences are (1,5,6,2) and (1,5,5,1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
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Cite This Article
METE, P., ZENGİN, E. E. (2019). Minimal free resolutions of the tangent cones for Gorenstein monomial curves. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 6, 2782–2793. https://ajindex.com/articles/198153