On the Hilbert vector of the Jacobian module of a plane curve

Armando Cerminara; Alexandru Dimca; Giovanna Ilardi

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arXiv · 1905.04055

On the Hilbert vector of the Jacobian module of a plane curve

Armando Cerminara·Alexandru Dimca·Giovanna Ilardi

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Abstract

We identify several classes of curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 vector bundles on $\mathbb{P}^2$, is used to get a sharp lower bound for the initial degree of the Jacobian module $N(f)$, under a semistability condition.

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Armando Cerminara, Alexandru Dimca, Giovanna Ilardi. 2019-05-10. On the Hilbert vector of the Jacobian module of a plane curve. https://arxiv.org/abs/1905.04055

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