Syzygies and logarithmic vector fields along plane curves
Journal de l’École polytechnique - Mathématiques, Volume 1  (2014), p. 247-267

We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a plane curve C and the stability of the sheaf of logarithmic vector fields along C, the freeness of the divisor C and the Torelli properties of C (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 C et la stabilité du faisceau des champs de vecteurs logarithmiques le long de C, la liberté du diviseur C et les propriétés de Torelli de C (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.

DOI : https://doi.org/10.5802/jep.10
Classification:  14C34,  14H50,  32S05
Keywords: Syzygy, plane curve, logarithmic vector fields, stable bundle, free divisor, Torelli property
@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},
     publisher = {Ecole polytechnique},
     volume = {1},
     year = {2014},
     pages = {247-267},
     doi = {10.5802/jep.10},
     language = {en},
     url = {http://www.numdam.org/item/JEP_2014__1__247_0}
}
Dimca, Alexandru; Sernesi, Edoardo. 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. http://www.numdam.org/item/JEP_2014__1__247_0/

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