Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves

Alexandru Dimca
G. Ilardi
  • Fonction : Auteur
G. Sticlaru
  • Fonction : Auteur

Résumé

Let $C:f=0$ be a reduced curve in the complex projective plane. The minimal degree $mdr(f)$ of a Jacobian syzygy for $f$, which is the same as the minimal degree of a derivation killing $f$, is an important invariant of the curve $C$, for instance it can be used to determined whether $C$ is free or nearly free. In this note we study the relations of this invariant $mdr(f)$ with a decomposition of $C$ as a union of two curves $C_1$ and $C_2$, without common irreducible components. When all the singularities that occur are quasihomogeneous, a result by Schenck, Terao and Yoshinaga yields finer information on this invariant in this setting. Using this, we give some geometrical criteria, the first ones of this type in the existing literature as far as we know, for a line to be a jumping line for the rank 2 vector bundle of logarithmic vector fields along a reduced curve $C$.

Dates et versions

hal-03531136 , version 1 (18-01-2022)

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Citer

Alexandru Dimca, G. Ilardi, G. Sticlaru. Addition-deletion results for the minimal degree of a Jacobian syzygy of a union of two curves. 2022. ⟨hal-03531136⟩
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