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A computational
approach to higher Jacobian ideals
Tabitha Ramirez, Hao Shen and Fei Ye |
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Vol. 18 (2025), No. 5, 873–883
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Abstract |
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Employing a technique involving Kronecker tensor and matrix vectorization, we compute the second order Jacobian ideal of a hypersurface . Our calculations reveal that the Jacobian ideal, when considered modulo the ideal , undergoes a decomposition where a power of the Jacobian ideal becomes a factor. As an application, we confirm a conjecture of Hussain, Ma, Yau and Zuo (J. Algebra 618 (2023), 165–194, Conjecture 1.5) for a hypersurface with an isolated singularity in . |
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Keywords
Nash blow-up, higher Jacobian ideal, hypersurface
singularity
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Mathematical Subject Classification
Primary: 14B05, 32S05
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Milestones
Received: 12 January 2024
Revised: 13 May 2024
Accepted: 15 May 2024
Published: 20 November 2025
Communicated by Ravi Vakil
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Authors |
| Tabitha Ramirez | |
| The City College of New York New York, NY United States |
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| Hao Shen | |
| Hamilton College Clinton, NY United States |
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| Fei Ye | |
| Department of Mathematics and
Computer Science Queensborough Community College of CUNY New York, NY United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
