Raynaud vector bundles

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We construct vector bundles \({R^{rk}_{\mu}}\) 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 \({\iff}\)\({{\rm Hom}(R^{rk}_{\mu}, E) = 0}\). As a byproduct of our construction we obtain effective bounds on r such that the linear system |R·Θ| has base points on UX(r, r(g − 1)).