On the Generic vanishing of certain Koszul cohomology groups

Details On the Generic vanishing of certain Koszul cohomology groups On the Generic vanishing of certain Koszul cohomology groups

2011-08-23

arxiv.org/abs/1108.4714v2

Mathematics

Algebraic Geometry

21 pages. minor updates

Scientific paper

We propose a new approach to study Koszul cohomology of general $g^r_d$'s on general curves via degenerations and deformations. As an application of this new method, we prove projective normality for general line bundles $L$ on general curves with $h^1(L)\le1$ and degree greater than roughly $(5/4)g$. This improves the bound in a classical theorem of Green and Lazarsfeld. Also we give some partial results on vanishing of higher syzygies for line bundles with $h^1(L)=1$.

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