On the gonality sequence of an algebraic curve

2010/07/15 by Herbert Lange, H. Lange, Lange, H. +3
Arts and Humanities · Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1007.2542

arxiv created 2010/07/15 · openalex publication_date 2010/07/15 · arxiv updated 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any smooth irreducible projective curve X, the gonality sequence \d_r | r ∈ \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 \PP³.

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