We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a plane curve and the stability of the sheaf of logarithmic vector fields along , the freeness of the divisor and the Torelli properties of (in the sense of Dolgachev-Kapranov). We show in particular that curves with a small number of nodes and cusps are Torelli in this sense.
Nous étudions les relations entre les syzygies de l’idéal jacobien associé à l’équation définissant une courbe plane et la stabilité du faisceau des champs de vecteurs logarithmiques le long de , la liberté du diviseur et les propriétés de Torelli de (au sens de Dolgachev-Kapranov). Nous montrons en particulier que les courbes ayant un petit nombre de points doubles et de cusps ont la propriété de Torelli.
Accepted:
Published online:
DOI: 10.5802/jep.10
Keywords: Syzygy, plane curve, logarithmic vector fields, stable bundle, free divisor, Torelli property
Mot clés : Syzygie, courbe plane, champ de vecteurs logarithmique, fibré stable, diviseur libre, propriété de Torelli
Alexandru Dimca 1; Edoardo Sernesi 2
CC-BY-ND 4.0
@article{JEP_2014__1__247_0,
author = {Alexandru Dimca and Edoardo Sernesi},
title = {Syzygies and logarithmic vector fields along plane curves},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {247--267},
publisher = {\'Ecole polytechnique},
volume = {1},
year = {2014},
doi = {10.5802/jep.10},
mrnumber = {3322789},
zbl = {1327.14049},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.10/}
}
TY - JOUR AU - Alexandru Dimca AU - Edoardo Sernesi TI - Syzygies and logarithmic vector fields along plane curves JO - Journal de l’École polytechnique — Mathématiques PY - 2014 SP - 247 EP - 267 VL - 1 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.10/ DO - 10.5802/jep.10 LA - en ID - JEP_2014__1__247_0 ER -
%0 Journal Article %A Alexandru Dimca %A Edoardo Sernesi %T Syzygies and logarithmic vector fields along plane curves %J Journal de l’École polytechnique — Mathématiques %D 2014 %P 247-267 %V 1 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.10/ %R 10.5802/jep.10 %G en %F JEP_2014__1__247_0
Alexandru Dimca; Edoardo Sernesi. Syzygies and logarithmic vector fields along plane curves. Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 247-267. doi : 10.5802/jep.10. https://jep.centre-mersenne.org/articles/10.5802/jep.10/
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