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摘要翻译：
证明了完全线性系统在$k3$曲面上光滑曲线间的倾角除Donagi-Morrison例子外是常数。Ciliberto和Pareschi在线性系统充分的附加条件下证明了这一点。因此，我们证明了$K3$曲面上的例外曲线满足Eisenbud-Lange-Martens-Schreyer猜想，并显式地描述了这类曲线。它们被证明是Eisenbud-Lange-Martens-Schreyer在$k3$曲面上的异常曲线例子的自然延伸。
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英文标题：
《On two conjectures for curves on $K3$ surfaces》
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作者：
Andreas Leopold Knutsen
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0705.0302
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