Manuscripta Mathematica

, Volume 137, Issue 3–4, pp 457–473 | Cite as

On the gonality sequence of an algebraic curve

  • H. LangeEmail author
  • G. Martens


For any smooth irreducible projective curve X, the gonality sequence \({\{d_r \;| \; r \in \mathbb N\}}\) is a strictly increasing sequence of positive integer invariants of X. In most known cases d r+1 is not much bigger than d r . In our terminology this means the numbers d r satisfy the slope inequality. It is the aim of this paper to study cases when this is not true. We give examples for this of extremal curves in \({{\mathbb P}^r}\), for curves on a general K3-surface in \({{\mathbb P}^r}\) and for complete intersections in \({{\mathbb P}^3}\).

Mathematics Subject Classification (2000)

Primary: 14H45 Secondary: 14H51 32L10 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany

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