On two conjectures for curves on K3 surfaces

2007/05/02 by Andreas Leopold Knutsen, Knutsen, Andreas Leopold
Mathematics · #14H51 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0705.0302

openalex publication_date 2007/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the gonality among the smooth curves in a complete linear system on a K3 surface is constant except for the Donagi-Morrison example. This was proved by Ciliberto and Pareschi under the additional condition that the linear system is ample. As a consequence we prove that exceptional curves on K3 surfaces satisfy the Eisenbud-Lange-Martens-Schreyer conjecture and explicitly describe such curves. They turn out to be natural extensions of the Eisenbud-Lange-Martens-Schreyer examples of exceptional curves on K3 surfaces.

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