Comptes Rendus
no. 4
Algebraic Geometry
Green–Lazarsfeld's conjecture for generic curves of large gonality
[La conjecture de Green–Lazarsfeld pour les courbes génériques de gonalité élevée]

Présenté par : Jean-Pierre Demailly

Marian Aprodu1, 2 ; Claire Voisin3
1 Université de Grenoble 1, laboratoire de mathématiques, institut Fourier, BP 74, 38402 Saint Martin d'Hères cedex, France
2 Romanian Academy, Institute of Mathematics “Simion Stoilow”, PO Box 1-764, 70700, Bucharest, Romania
3 Université Paris 7 Denis Diderot, CNRS UMR 7586, institut de mathématiques, 2, place Jussieu, 75251 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 335-339.

We use Green's canonical syzygy conjecture for generic curves to prove that the Green–Lazarsfeld gonality conjecture holds for generic curves of genus g, and gonality d, if g/3<d<[g/2]+2.

Nous utilisons la conjecture de Green sur les syzygies canoniques des courbes génériques pour démontrer la conjecture de la gonalité de Green–Lazarsfeld pour les courbes génériques de genre g et gonalité d, avec g/3<d<[g/2]+2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00062-1

Marian Aprodu 1, 2 ; Claire Voisin 3

1 Université de Grenoble 1, laboratoire de mathématiques, institut Fourier, BP 74, 38402 Saint Martin d'Hères cedex, France
2 Romanian Academy, Institute of Mathematics “Simion Stoilow”, PO Box 1-764, 70700, Bucharest, Romania
3 Université Paris 7 Denis Diderot, CNRS UMR 7586, institut de mathématiques, 2, place Jussieu, 75251 Paris cedex 05, France 
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Marian Aprodu; Claire Voisin. Green–Lazarsfeld's conjecture for generic curves of large gonality. Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 335-339. doi : 10.1016/S1631-073X(03)00062-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00062-1/

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