On the Hilbert vector of the Jacobian module of a plane curve
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 3syzygy 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.04055
 Bibcode:
 2019arXiv190504055C
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 10 pages, 4 figures. To appear in Portugaliae Mathematica