## Kyoto Journal of Mathematics

### On bundles of rank $3$ computing Clifford indices

#### Abstract

Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to[4] semistable bundles of any rank. Recent work has been focused mainly on the rank-$2$ Clifford index, although interesting results have also been obtained for the case of rank $3$. In this paper we extend this work, obtaining improved lower bounds for the rank-$3$ Clifford index. This allows the first computations of the rank-$3$ index in nontrivial cases and examples for which the rank-$3$ index is greater than the rank-$2$ index.

#### Article information

Source
Kyoto J. Math., Volume 53, Number 1 (2013), 25-54.

Dates
First available in Project Euclid: 25 March 2013

https://projecteuclid.org/euclid.kjm/1364218040

Digital Object Identifier
doi:10.1215/21562261-1966062

Mathematical Reviews number (MathSciNet)
MR3049306

Zentralblatt MATH identifier
1307.14052

#### Citation

Lange, H.; Newstead, P. E. On bundles of rank $3$ computing Clifford indices. Kyoto J. Math. 53 (2013), no. 1, 25--54. doi:10.1215/21562261-1966062. https://projecteuclid.org/euclid.kjm/1364218040

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