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On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface

$icon-email$ Edoardo Ballico

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 $L \in {Pic}^{t} (C)$ with $h^{0} (C, L) = r + 1$ . In this paper, for all $g \geq 40805$ we construct several examples of smooth curves $C$ of genus $g$ with $d_{3} (C) / 3 < d_{4} (C) / 4$ , i.e., for which a slope inequality fails.

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On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface

Abstract