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Affine Flag Manifolds and Principal Bundles pp 165–202Cite as

Clifford Indices for Vector Bundles on Curves

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Part of the book series: Trends in Mathematics ((TM))

Abstract

For smooth projective curves of genus g ≥ 4, the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper we generalise this to introduce Clifford indices for semistable vector bundles on curves. We study these invariants, giving some basic properties and carrying out some computations for small ranks and for general and some special curves. For curves whose classical Clifford index is two, we compute all values of our new Clifford indices.

Both authors are members of the research group VBAC (Vector Bundles on Algebraic Curves). The second author would like to thank the Department Mathematik der Universität Erlangen-Nürnberg for its hospitality.

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Author information

Authors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Bismarckstraße 1 11/2, D-91054, Erlangen, Germany

    Herbert Lange

  2. Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool, L69 7ZL, UK

    Peter E. Newstead

Authors
  1. Herbert Lange
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  2. Peter E. Newstead
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Alexander Schmitt

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Lange, H., Newstead, P.E. (2010). Clifford Indices for Vector Bundles on Curves. In: Schmitt, A. (eds) Affine Flag Manifolds and Principal Bundles. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0288-4_6

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