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

Journal of the European Mathematical Society (2002)

- Volume: 004, Issue: 4, page 363-404
- ISSN: 1435-9855

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topVoisin, 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 -

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