Publication: Bounding sections of bundles on curves
No Thumbnail Available
Full text at PDC
Advisors (or tutors)
Cambridge University Press
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).