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<p>We show that the second Jacobian ideal of a hypersurface can be decomposed such that a power of the Jacobian ideal becomes a factor. As an application of the decomposition, we present an elementary proof establishing that the second Nash blow-up algebra of a hypersurface singularity is a contact invariant.</p>

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On the structure of second Jacobian ideals

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Fei Ye

摘要

We show that the second Jacobian ideal of a hypersurface can be decomposed such that a power of the Jacobian ideal becomes a factor. As an application of the decomposition, we present an elementary proof establishing that the second Nash blow-up algebra of a hypersurface singularity is a contact invariant.