Geodesic
Syzygies and logarithmic vector fields along plane curves
[Syzygies et champs de vecteurs logarithmiques le long de courbes planes]
Dimca, Alexandru1  ; Sernesi, Edoardo2 
1 Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351 Parc Valrose, 06108 Nice, Cedex 02, France
2 Dipartimento di Matematica e Fisica, Università Roma Tre, Largo S. L. Murialdo 1, 00146 Roma, Italy
Journal de l’École polytechnique — Mathématiques, Tome 1 (2014), pp. 247-267.

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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 : 10.5802/jep.10
Classification : 14C34, 14H50, 32S05
Keywords: Syzygy, plane curve, logarithmic vector fields, stable bundle, free divisor, Torelli property
Mots-clés : Syzygie, courbe plane, champ de vecteurs logarithmique, fibré stable, diviseur libre, propriété de Torelli

Dimca, Alexandru 1 ; Sernesi, Edoardo 2

1 Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351 Parc Valrose, 06108 Nice, Cedex 02, France
2 Dipartimento di Matematica e Fisica, Università Roma Tre, Largo S. L. Murialdo 1, 00146 Roma, Italy
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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://geodesic.mathdoc.fr/articles/10.5802/jep.10/

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