Abstract
Let C be a smooth curve of degree \(d_0\) lying on a smooth surface in projective space. Exploiting a criterion due to I. Reider we study when the divisors in a linear series of degree \(d \le d_0\) on C are contained in hyperplanes. For a K3 surface S with Picard group \({\mathbb {Z}}^2\) we succeed if S contains a line.
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Martens, G. On curves on K3 surfaces: III. Arch. Math. 115, 401–412 (2020). https://doi.org/10.1007/s00013-020-01496-7
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DOI: https://doi.org/10.1007/s00013-020-01496-7