Green's generic syzygy conjecture for curves of even genus lying on a K3 surface
Voisin, Claire
HAL, hal-00021784 / Harvested from HAL
Text on HAL
We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: {\it For a smooth projective curve $C$ of genus $g$ in characteristic 0, the condition ${\rm Cliff} C>l$ is equivalent to the fact that $K_{g-l'-2,1}(C,K_C)=0, \forall l'\leq l$.} We propose a new approach, which allows up to prove this result for generic curves $C$ of genus $g(C)$ and gonality ${\rm gon(C)}$ in the range $$\frac{g(C)}{3}+1\leq {\rm gon(C)}\leq\frac{g(C)}{2}+1.$$
Publié le : 2002-07-05
Classification:  [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 
@article{hal-00021784,
     author = {Voisin, Claire},
     title = {Green's generic syzygy conjecture for curves of even genus lying on a K3 surface},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00021784}
}

Voisin, Claire. Green's generic syzygy conjecture for curves of even genus lying on a K3 surface. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021784/