Self-duality of the local cohomology of the Jacobian ring and Gherardelli's Theorem

Davide Franco

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arXiv · 2001.03345

Self-duality of the local cohomology of the Jacobian ring and Gherardelli's Theorem

Davide Franco

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Abstract

We prove that the $0$-th local cohomology of the jacobian ring of a projective hypersurface with isolated singularities has a nice interpretation it in the context of linkage theory. Roughly speaking, it represents a measure of the failure of Gherardelli's theorem for the corresponding graded modules. This leads us to a different and characteristic free proof of its self-duality, which turns out to be an easy consequence of Grothendieck's local duality theorem.

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Davide Franco. 2020-01-10. Self-duality of the local cohomology of the Jacobian ring and Gherardelli's Theorem. https://arxiv.org/abs/2001.03345

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