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Archiv der Mathematik

, Volume 99, Issue 1, pp 25–31 | Cite as

On the gonality sequence of smooth curves

  • Edoardo Ballico
Article
  • 96 Downloads

Abstract

Let C be a smooth curve of genus g. For each positive integer r the r-gonality d r (C) of C is the minimal integer t such that there is \({L\in {\rm Pic}^t(C)}\) with h 0(C, L) = r + 1. Here we use nodal plane curves to construct several smooth curves C with d 2(C)/2 < d 3(C)/3, i.e., for which a slope inequality fails.

Mathematics Subject Classification (2010)

14H45 14H50 32L10 

Keywords

Gonality sequence Smooth curve Nodal curve 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TrentoPovoItaly

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