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Article Dans Une Revue Publicacions Matem\`atiques Année : 2020

On the jumping lines of bundles of logarithmic vector fields along plane curves

Résumé

For a reduced curve $C:f=0$ in the complex projective plane $\mathbb{P}^2$, we study the set of jumping lines for the rank two vector bundle $T\langle C \rangle $ on $\mathbb{P}^2$, whose sections are the logarithmic vector fields along $C$. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of $f$ and with the Bourbaki ideal of the module of Jacobian syzygies of $f$. In particular, when the vector bundle $T\langle C \rangle $ is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne and Hulek resurface in the study of this special class of rank two vector bundles.

Dates et versions

hal-01951978 , version 1 (11-12-2018)

Identifiants

Citer

Alexandru Dimca, Gabriel Sticlaru. On the jumping lines of bundles of logarithmic vector fields along plane curves. Publicacions Matem\`atiques, 2020, 64 (2), pp.513-542. ⟨10.5565/PUBLMAT6422006⟩. ⟨hal-01951978⟩
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