Smooth Curves on Projective K3 Surfaces
DOI:
https://doi.org/10.7146/math.scand.a-14371Abstract
In this paper we give for all n≥2, d>0, g≥0 necessary and sufficient conditions for the existence of a pair (X,C), where X is a K3 surface of degree 2n in Pn+1 and C is a smooth (reduced and irreducible) curve of degree d and genus g on X. The surfaces constructed have Picard group of minimal rank possible (being either 1 or 2), and in each case we specify a set of generators. For n≥4 we also determine when X can be chosen to be an intersection of quadrics (in all other cases X has to be an intersection of both quadrics and cubics). Finally, we give necessary and sufficient conditions for OC(k) to be non-special, for any integer k≥1.Downloads
Published
2002-06-01
How to Cite
Knutsen, A. L. (2002). Smooth Curves on Projective K3 Surfaces. MATHEMATICA SCANDINAVICA, 90(2), 215–231. https://doi.org/10.7146/math.scand.a-14371
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