[La conjecture de Green–Lazarsfeld pour les courbes génériques de gonalité élevée]
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.
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.
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@article{CRMATH_2003__336_4_335_0,
author = {Aprodu, Marian and Voisin, Claire},
title = {Green{\textendash}Lazarsfeld's conjecture for generic curves of large gonality},
journal = {Comptes Rendus. Math\'ematique},
pages = {335--339},
publisher = {Elsevier},
volume = {336},
number = {4},
year = {2003},
doi = {10.1016/S1631-073X(03)00062-1},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00062-1/}
}
TY - JOUR AU - Aprodu, Marian AU - Voisin, Claire TI - Green–Lazarsfeld's conjecture for generic curves of large gonality JO - Comptes Rendus. Mathématique PY - 2003 SP - 335 EP - 339 VL - 336 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00062-1/ DO - 10.1016/S1631-073X(03)00062-1 LA - en ID - CRMATH_2003__336_4_335_0 ER -
%0 Journal Article %A Aprodu, Marian %A Voisin, Claire %T Green–Lazarsfeld's conjecture for generic curves of large gonality %J Comptes Rendus. Mathématique %D 2003 %P 335-339 %V 336 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00062-1/ %R 10.1016/S1631-073X(03)00062-1 %G en %F CRMATH_2003__336_4_335_0
Aprodu, Marian; Voisin, Claire. Green–Lazarsfeld's conjecture for generic curves of large gonality. Comptes Rendus. Mathématique, Tome 336 (2003) no. 4, pp. 335-339. doi : 10.1016/S1631-073X(03)00062-1. http://www.numdam.org/articles/10.1016/S1631-073X(03)00062-1/
[1] On the vanishing of higher syzygies of curves, Math. Z., Volume 241 (2002), pp. 1-15
[2] Hilbert functions and Betti numbers in a flat family, Ann. Mat. Pura Appl. (4), Volume 142 (1985), pp. 277-292
[3] Syzygies of points in projective space and applications (Orecchia; Ferruccio et al., eds.), Zero-Dimensional Schemes, Proceedings of the International Conference Held in Ravello, Italy, June 8–13, 1992, de Gruyter, Berlin, 1994, pp. 145-170
[4] Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math., Volume 90 (1969), pp. 541-575
[5] Koszul cohomology and the geometry of projective varieties, J. Differential Geom., Volume 19 (1984), pp. 125-171 (With an Appendix by M. Green and R. Lazarsfeld)
[6] Koszul cohomology and the geometry of projective varieties. II, J. Differential Geom., Volume 20 (1984), pp. 279-289
[7] On the projective normality of complete linear series on an algebraic curve, Invent. Math., Volume 83 (1986), pp. 73-90
[8] Green's conjecture for the generic r-gonal curve of genus g⩾3r−7, Duke Math. J., Volume 111 (2002), pp. 363-404
[9] Green's generic syzygy conjecture for curves of even genus lying on a K3 surface, J. European Math. Soc., Volume 4 (2002), pp. 363-404
[10] C. Voisin, Green's canonical syzygy conjecture for generic curves of odd genus, Preprint, | arXiv
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