Sols Lucía, IgnacioArrondo Esteban, EnriqueEllingsrud, G.Peskine, C.Sacchiero, G.Stromme, S. A.2023-06-202023-06-2019920-521-43352-5https://hdl.handle.net/20.500.14352/60667The aim of this note is to prove some bounds on the global sections of vector bundles over a smooth, complete and connected curve C . Just by an application of the Clifford theorem, the authors prove (Proposition 2) (*) h 0 (E)≤deg(E)/2+2 for a semistable rank 2 vector bundle E and discuss when (*) is sharp. They propose a sharper bound for an indecomposable bundle (which is shown to be correct for a hyperelliptic curve) but, as added in proof, this bound is overoptimistic in the general case (see Proposition IV.7 of a paper by the reviewer [Duke Math. J. 64 (1991), no. 2, 333–347] or forthcoming work of Tan). By a dimension count the authors prove (Corollary 6) h 0 (E)≤deg(E)/2+rank(E) for every globally generated semistable bundle E . In this set-up, they give a Martens-type theorem (Proposition 9).book parthttp://www.cambridge.org/gb/knowledge/isbn/printView/item6532865/?site_locale=en_GBhttp://www.cambridge.org/metadata only access512Ruled surfaceHyperelliptic curvesNon-semistable vector bundlesÁlgebra1201 Álgebra