Green's generic syzygy conjecture for curves of even genus lying on a K3 surface

Voisin, Claire. "Green's generic syzygy conjecture for curves of even genus lying on a K3 surface." Journal of the European Mathematical Society 004.4 (2002): 363-404. <http://eudml.org/doc/277308>.

@article{Voisin2002,
abstract = {We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: For a smooth projective curve $C$ of genus $g$ in characteristic 0, the condition $\text\{Cliff\} C>l$ is equivalent to the fact that $K_\{g-l^\{\prime \}-2,1\}(C,K_C)=0, \forall l^\{\prime \}\le l$. We propose a new approach, which allows up to prove this result for generic curves $C$ of genus $g(C)$ and gonality $\text\{gon(C)\}$ in the range \[\frac\{g(C)\}\{3\}+1\le \text\{gon(C)\}\le \frac\{g(C)\}\{2\}+1.\]},
author = {Voisin, Claire},
journal = {Journal of the European Mathematical Society},
keywords = {syzygy conjecture; K3 surface},
language = {eng},
number = {4},
pages = {363-404},
publisher = {European Mathematical Society Publishing House},
title = {Green's generic syzygy conjecture for curves of even genus lying on a K3 surface},
url = {http://eudml.org/doc/277308},
volume = {004},
year = {2002},
}

TY - JOUR
AU - Voisin, Claire
TI - Green's generic syzygy conjecture for curves of even genus lying on a K3 surface
JO - Journal of the European Mathematical Society
PY - 2002
PB - European Mathematical Society Publishing House
VL - 004
IS - 4
SP - 363
EP - 404
AB - We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: For a smooth projective curve $C$ of genus $g$ in characteristic 0, the condition $\text{Cliff} C>l$ is equivalent to the fact that $K_{g-l^{\prime }-2,1}(C,K_C)=0, \forall l^{\prime }\le l$. We propose a new approach, which allows up to prove this result for generic curves $C$ of genus $g(C)$ and gonality $\text{gon(C)}$ in the range \[\frac{g(C)}{3}+1\le \text{gon(C)}\le \frac{g(C)}{2}+1.\]
LA - eng
KW - syzygy conjecture; K3 surface
UR - http://eudml.org/doc/277308
ER -