RT Book, Section
T1 Bounding sections of bundles on curves
A1 Sols Lucía, Ignacio
A1 Arrondo Esteban, Enrique
A2 Ellingsrud, G.
A2 Peskine, C.
A2 Sacchiero, G.
A2 Stromme, S. A.
AB 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).
PB Cambridge University Press
SN 0-521-43352-5
YR 1992
FD 1992
LK https://hdl.handle.net/20.500.14352/60667
UL https://hdl.handle.net/20.500.14352/60667
DS Docta Complutense
RD 10 abr 2025