%0 Book Section
%T Bounding sections of bundles on curves
publisher Cambridge University Press
%D 1992
%U 0-521-43352-5
%@ https://hdl.handle.net/20.500.14352/60667
%X The 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).
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