[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.
Accepté le :
Publié le :
Marian Aprodu 1, 2 ; Claire Voisin 3
@article{CRMATH_2003__336_4_335_0,
author = {Marian Aprodu and Claire Voisin},
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},
}
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/
[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
- A Hurwitz divisor on the moduli of Prym curves, Geometriae Dedicata, Volume 216 (2022) no. 1 | DOI:10.1007/s10711-021-00663-6
- Asymptotic Syzygies and Higher Order Embeddings, International Mathematics Research Notices, Volume 2022 (2022) no. 4, p. 2934 | DOI:10.1093/imrn/rnaa208
- Linear syzygies of curves with prescribed gonality, Advances in Mathematics, Volume 356 (2019), p. 106810 | DOI:10.1016/j.aim.2019.106810
- The gonality conjecture on syzygies of algebraic curves of large degree, Publications mathématiques de l'IHÉS, Volume 122 (2015) no. 1, p. 301 | DOI:10.1007/s10240-015-0072-2
- Asymptotic syzygies of algebraic varieties, Inventiones mathematicae, Volume 190 (2012) no. 3, p. 603 | DOI:10.1007/s00222-012-0384-5
- Green’s conjecture for curves on arbitrary K3 surfaces, Compositio Mathematica, Volume 147 (2011) no. 3, p. 839 | DOI:10.1112/s0010437x10005099
- The Green Conjecture for Exceptional Curves on a K3 Surface, International Mathematics Research Notices (2010) | DOI:10.1093/imrn/rnn043
- Koszul cohomology and singular curves, Rendiconti del Circolo Matematico di Palermo, Volume 59 (2010) no. 1, p. 121 | DOI:10.1007/s12215-010-0008-0
-
- SINGULAR CURVES ON A K3 SURFACE AND LINEAR SERIES ON THEIR NORMALIZATIONS, International Journal of Mathematics, Volume 18 (2007) no. 06, p. 671 | DOI:10.1142/s0129167x0700428x
Cité par 10 documents. Sources : Crossref
Commentaires - Politique