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Alexandru Dimca; Edoardo Sernesi
Syzygies and logarithmic vector fields along plane curves
(Syzygies et champs de vecteurs logarithmiques le long de courbes planes)
Journal de l'École polytechnique — Mathématiques, 1 (2014), p. 247-267, doi: 10.5802/jep.10
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Class. Math.: 14C34, 14H50, 32S05
Mots clés: Syzygie, courbe plane, champ de vecteurs logarithmique, fibré stable, diviseur libre, propriété de Torelli

Résumé - Abstract

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.

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