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A characterization of ample vector bundles on a curve. (English) Zbl 0728.14033

Let C be a smooth curve and E be an ample vector bundle on C. The authors show that there is a finite map f: C\({}'\to C\) with the following properties: On \(C'\), there is a line bundle L of positive degree and we have a surjective map \(\otimes^{s}_{i}L \to f^*E\). In particular, one may even assume that L is generated by its sections. - The rough idea of the proof is the following: First the authors use induction and the Harder-Narasimhan filtration to reduce the problem to the case when E is semistable. Then one knows the ample line bundles on the projectivized bundle P(E). Now one constructs the covering by considering high degree complete intersections in P(E).
Reviewer: L.Ein (Chicago)

MSC:

14H60 Vector bundles on curves and their moduli
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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References:

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