Abstract
We study the Clifford index c of a smooth irreducible curve X in the linear series |2H| on a special K3 surface S of degree 2n in \({{\mathbb P}}^{n+1}\), with hyperplane section H, and we look for the complete and base point free linear series of S whose restrictions to X compute c. In a more general context, we discuss the features of such series, for an assigned curve on a K3 surface; this discussion is of some independent interest.
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Martens, G. On curves on K3 surfaces, II. Arch. Math. 110, 35–43 (2018). https://doi.org/10.1007/s00013-017-1094-4
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DOI: https://doi.org/10.1007/s00013-017-1094-4