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arXiv · 1007.2542

On the gonality sequence of an algebraic curve

H. Lange·G. Martens
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Abstract

For any smooth irreducible projective curve $X$, the gonality sequence $\{d_r \;| \; r \in \mathbb N \}$ 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 $\PP^3$.

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H. Lange, G. Martens. 2010-07-15. On the gonality sequence of an algebraic curve. https://arxiv.org/abs/1007.2542

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