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On kth-order embeddings of K3 surfaces and Enriques surfaces

Andreas Leopold Knutsen
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Abstract

We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big line bundle on a K3 surface to be birationally k-very ample and birationally k-spanned, and relate these concepts to the Clifford index and gonality of smooth curves in |L|.

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Andreas Leopold Knutsen. 2000-12-25. On kth-order embeddings of K3 surfaces and Enriques surfaces. https://arxiv.org/abs/math/0008169

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