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

Edoardo Ballico

paper

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

arXiv:1303.0097

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 $L \in P i c^{t} (C)$ 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.

Accepted on Acta Math. Viet