Abstract
Given integers \(g \geq 2\) and \(0 \leq c \leq \lfloor \frac{g-1}{2} \rfloor\), one may ask whether there actually exists a pair (S,L), where S is a K3 surface, L 2 = 2g – 2 and all smooth curves in |L| have Clifford index c.
Theorem 4.1 below gives a positive answer to this question. Theorem 4.4 below answers the same kind of question concerning the possible gonalities of a curve on a K3 surface.
The results in this chapter were first given in [Kn3]. We also include the material here, to obtain a complete exposition.
Mathematics Subject Classification (2000):
- 14J28
- 14H51
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© 2004 Springer-Verlag Berlin/Heidelberg
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Johnsen, T., Knutsen, A.L. (2004). 4. Two existence theorems. In: K3 Projective Models in Scrolls. Lecture Notes in Mathematics, vol 1842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40898-7_4
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DOI: https://doi.org/10.1007/978-3-540-40898-7_4
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