# Raynaud vector bundles

Georg Hein

Number | 11 |
---|---|

Author | Georg Hein |

Year | 2007 |

We construct vector bundles R_{μ}^{rk} on a smooth projective curve X having the property that for all sheaves E of slope μ and rank rk on X we have an equivalence:

E is a semistable vector bundle <=> Hom(R_{μ}^{rk},E) = 0.

As a byproduct of our construction we obtain effective bounds on r such that the linear system |R · Θ| has base points on U_{X}(r, r(g − 1)).