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. 311–325DOI 10.4171/PM/2038