Splitting curves on a rational ruled surface, the Mordell-Weil groups of hyperelliptic fibrations and Zariski pairs
| dc.creator | Tokunaga, Hiro-o | |
| dc.date | 2009-05-01 | |
| dc.date.accessioned | 2026-07-07T13:10:58Z | |
| dc.date.available | 2026-07-07T13:10:58Z | |
| dc.description | Let $Σ$ be a smooth projective surface, let $f' : S' \to Σ$ be a double cover of $Σ$ and let $μ: S \to S'$ be the canonical resolution. Put $f = f'\circμ$. An irreducible curve $C$ on $Σ$ is said to be a splitting curve with respect to $f$ if $f^*C$ is of the form $C^+ + C^- + E$, where $C^- = σ_f^*C^+$, $σ_f$ being the covering transformation of $f$ and all irreducible components of $E$ are contained in the exceptional set of $μ$. In this article, we show that a kind of "reciprocity" of splitting curves holds for a certain pair of curves on rational ruled surfaces. As an application, we consider the topology of the complements of certain curves on rational ruled surfaces. | |
| dc.description | 23pages | |
| dc.identifier | https://arxiv.org/abs/0905.0047 | |
| dc.identifier | http://arxiv.org/abs/0905.0047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229151 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14H30, 14J26, 14J27 | |
| dc.title | Splitting curves on a rational ruled surface, the Mordell-Weil groups of hyperelliptic fibrations and Zariski pairs | |
| dc.type | text |