Smooth Curves on Projective K3 Surfaces

Authors

  • Andreas Leopold Knutsen

DOI:

https://doi.org/10.7146/math.scand.a-14371

Abstract

In this paper we give for all n2, d>0, g0 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 n4 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 k1.

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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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Articles