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On the gonality sequence of smooth curves

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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.

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  1. Department of Mathematics, University of Trento, 38123, Povo, TN, Italy

    Edoardo Ballico

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  1. Edoardo Ballico
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Correspondence to Edoardo Ballico.

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Partially supported by MIUR and GNSAGA (Italy).

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Ballico, E. On the gonality sequence of smooth curves. Arch. Math. 99, 25–31 (2012). https://doi.org/10.1007/s00013-012-0409-8

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  • DOI: https://doi.org/10.1007/s00013-012-0409-8

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