On two conjectures for curves on $K3$ surfaces
Algebraic Geometry
2007-05-23 v1
Abstract
We prove that the gonality among the smooth curves in a complete linear system on a 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 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 surfaces.
Cite
@article{arxiv.0705.0302,
title = {On two conjectures for curves on $K3$ surfaces},
author = {Andreas Leopold Knutsen},
journal= {arXiv preprint arXiv:0705.0302},
year = {2007}
}