On two conjectures for curves on $K3$ surfaces

Details On two conjectures for curves on $K3$ surfaces On two conjectures for curves on $K3$ surfaces

2007-05-02

arxiv.org/abs/0705.0302v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On two conjectures for curves on $K3$ surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On two conjectures for curves on $K3$ surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On two conjectures for curves on $K3$ surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-674975