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Sols, Ignacio and Arrondo Esteban, Enrique
(1992)
*Bounding sections of bundles on curves.*
In
Complex projective geometry.
London Mathematical Society Lecture Note Series
(179).
Cambridge University Press , Trieste, pp. 24-31.
ISBN 0-521-43352-5

Official URL: http://www.cambridge.org/gb/knowledge/isbn/printView/item6532865/?site_locale=en_GB

## Abstract

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).

Item Type: | Book Section |
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Uncontrolled Keywords: | Ruled surface; Hyperelliptic curves; Non-semistable vector bundles |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 20987 |

Deposited On: | 22 Apr 2013 15:47 |

Last Modified: | 22 Jan 2016 15:09 |

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