Singular curves on a K3 surface and linear series on their normalizations
| dc.creator | Flamini, Flaminio | |
| dc.creator | Knutsen, Andreas Leopold | |
| dc.creator | Pacienza, Gianluca | |
| dc.date | 2005-05-12 | |
| dc.date | 2006-09-19 | |
| dc.date.accessioned | 2026-07-07T06:39:56Z | |
| dc.date.available | 2026-07-07T06:39:56Z | |
| dc.description | In this paper, we study the Brill-Noether theory of the normalizations of singular, irreducible curves on a $K3$ surface. We introduce a {\em singular} Brill-Noether number $ρ_{sing}$ and show that if the Picard group of the K3 surface is ${\mathbb Z} [L]$, there are no $g^r_d$'s on the normalizations of irreducible curves in $|L|$, provided that $ρ_{sing} <0$. We give examples showing the sharpness of this result. We then focus on the case of {\em hyperelliptic normalizations}, and classify linear systems $|L|$ containing irreducible nodal curves with hyperelliptic normalizations, for $ρ_{sing}<0$, without any assumption on its Picard group. | |
| dc.description | 20 pages, remarks of the referee are added, to be published on International Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0505266 | |
| dc.identifier | http://arxiv.org/abs/math/0505266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101266 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H10, 14H51, 14J28, 14J60 | |
| dc.title | Singular curves on a K3 surface and linear series on their normalizations | |
| dc.type | text |