On the gonality sequence of an algebraic curve

H. Lange; G. Martens

paper

On the gonality sequence of an algebraic curve

arXiv:1007.2542

Abstract

For any smooth irreducible projective curve $X$ , the gonality sequence ${d_{r} ∣ r \in N}$ 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 $\PP^r$, for curves on a general K3-surface in $\PP^r$ and for complete intersections in $\PP^3$.