Raynaud vector bundles

Details Raynaud vector bundles Raynaud vector bundles

2007-06-27

arxiv.org/abs/0706.3970v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

We construct vector bundles $R^r_\mu$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $\iff$ $Hom(R^r_\mu,E)=0$. As a byproduct of our construction we obtain effective bounds on $r$ such that the linear system $|R \cdot \Theta|$ has base points on the moduli space $U_X(r,r(g-1))$.

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