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

2019/05/10 by Cerminara, Armando, Dimca, Alexandru, Ilardi, Giovanna
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04055

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 ℙ², 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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