Abstract:
We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or on an Enriques surface S 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 S to be birationally k-very ample and birationally k-spanned (our definition), and relate these concepts to the Clifford index and gonality of smooth curves in |L| and the existence of a particular type of rank 2 bundles on S.
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Received: 28 March 2000 / Revised version: 20 October 2000
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Knutsen, A. On kth-order embeddings of K3 surfaces and Enriques surfaces. manuscripta math. 104, 211–237 (2001). https://doi.org/10.1007/s002290170040
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DOI: https://doi.org/10.1007/s002290170040