On semistable vector bundles over curves

Biswas, Indranil ; Hein, Georg ; Hoffmann, Norbert (2008) On semistable vector bundles over curves Comptes Rendus Mathematique, 346 (17-18). pp. 981-984. ISSN 1631-073X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S16310...

Related URL: http://dx.doi.org/10.1016/j.crma.2008.07.016


Let X be a geometrically irreducible smooth projective curve defined over a field k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X,F⊗ E)=0 for i=0,1. We give an explicit bound for the rank of F. The proof uses a result of Popa for the case where k is algebraically closed.

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