On Two Conjectures for Curves on K3 Surfaces
نویسنده
چکیده
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 [CP] under the additional condition that the linear system is ample. As a consequence we prove that exceptional curves on K3 surfaces satisfy the EisenbudLange-Martens-Schreyer conjecture [ELMS] 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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