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.
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.
@article{JEP_2014__1__247_0,
author = {Dimca, Alexandru and Sernesi, Edoardo},
title = {Syzygies and logarithmic vector fields along plane curves},
journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
volume = {1},
year = {2014},
pages = {247-267},
doi = {10.5802/jep.10},
language = {en},
url = {http://dml.mathdoc.fr/item/JEP_2014__1__247_0}
}
Dimca, Alexandru; Sernesi, Edoardo. Syzygies and logarithmic vector fields along plane curves. Journal de l'École polytechnique - Mathématiques, Tome 1 (2014) pp. 247-267. doi : 10.5802/jep.10. http://gdmltest.u-ga.fr/item/JEP_2014__1__247_0/
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