Smooth curves on projective K3 surfaces
| dc.creator | Knutsen, Andreas Leopold | |
| dc.date | 1998-05-29 | |
| dc.date | 2001-06-07 | |
| dc.date.accessioned | 2026-07-07T05:24:53Z | |
| dc.date.available | 2026-07-07T05:24:53Z | |
| dc.description | In this paper we give for all $n \geq 2$, d>0, $g \geq 0$ necessary and sufficient conditions for the existence of a pair (X,C), where X is a K3 surface of degree 2n in $\matbf{P}^{n+1}$ 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 $n \geq 4$ 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 $Ø_C (k)$ to be non-special, for any integer $k \geq 1$. | |
| dc.description | 12 pages, to appear in Math. Scand. Mistake in earlier version of Thm 1.1 corrected and its proof is considerably simplified (removed the now redundant Sections 4 and 5 of the previous version). Added Rem. 1.2 and Prop. 1.3 | |
| dc.identifier | https://arxiv.org/abs/math/9805140 | |
| dc.identifier | http://arxiv.org/abs/math/9805140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76981 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Smooth curves on projective K3 surfaces | |
| dc.type | text |