On two conjectures for curves on $K3$ surfaces

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dc.creatorKnutsen, Andreas Leopold
dc.date2007-05-02
dc.date.accessioned2026-07-07T07:59:09Z
dc.date.available2026-07-07T07:59:09Z
dc.descriptionWe 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0705.0302
dc.identifierhttp://arxiv.org/abs/0705.0302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128260
dc.subjectAlgebraic Geometry
dc.subject14J26, 14H51
dc.titleOn two conjectures for curves on $K3$ surfaces
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