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

  • Armando Cerminara

    Università degli Studi di Napoli “Federico II”, Italy
  • Alexandru Dimca

    Université Côte d’Azur, Nice, France
  • Giovanna Ilardi

    Università degli Studi di Napoli “Federico II”, Italy
On the Hilbert vector of the Jacobian module of a plane curve cover

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Abstract

We identify several classes of complex projective plane curves , for which the Hilbert vector of the Jacobian module 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 , is used to get a sharp lower bound for the initial degree of the Jacobian module , under a semistability condition.

Cite this article

Armando Cerminara, Alexandru Dimca, Giovanna Ilardi, On the Hilbert vector of the Jacobian module of a plane curve. Port. Math. 76 (2019), no. 3/4, pp. 311–325

DOI 10.4171/PM/2038